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  • 1.
    Aksoy, A. G.
    et al.
    Department of Mathematics, Claremont McKenna College.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Real interpolation and measure of weak noncompactness1995In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 175, no 1, p. 5-12Article in journal (Refereed)
    Abstract [en]

    Behavior of weak measures of noncompactness under real interpolation is investigated. It is shown that "convexity type" theorems hold true for weak measures of noncompactness.

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  • 2.
    Aksoy, A.G.
    et al.
    Department of Mathematics Claremont McKenna College Claremont, CA 91711 USA.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lipschitz-Orlicz Spaces and the Laplace Equation1996In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 178, no 1, p. 81-101Article in journal (Refereed)
    Abstract [en]

    Stein and Taibleson gave a characterization for f ϵ Lp(ℝn) to be in the spaces Lip (α, Lp) and Zyg(α, Lp) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (α, Lm) and Zygmund-Orlicz spaces Zyg (φ, Lm) and to the general function φ ϵ P instead of the power function φ(t)= tα. Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces Lm (IRn). More general spaces δk(φ,X, q) are also considered.

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  • 3. Asekritova, Irina
    et al.
    Kruglyak, Natan
    Maligranda, Lech
    Nikolova, Ludmila
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lions-Peetre reiteration formulas for triples and their applications2001In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 145, no 3, p. 219-254Article in journal (Refereed)
    Abstract [en]

    Two reiteration theorems for triples of quasi-Banach function lattices are given. As a by-product of these, some interpolation results are obtained for block-Lorentz spaces and triples of weighted $L_p$-spaces.

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  • 4.
    Asekritova, Irina U.
    et al.
    Yaroslavl Pedagogical Institute.
    Kruglyak, Natan
    Maligranda, Lech
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Distribution and rearrangement estimates of the maximal function and interpolation1997In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 124, no 2, p. 107-132Article in journal (Refereed)
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  • 5.
    Astashin, S. V.
    et al.
    Samara State University, Russian Federation.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On interpolation in Lp spaces2003In: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 74, no 5-6, p. 734-739Article in journal (Refereed)
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  • 6.
    Astashkin, S.
    et al.
    Department of Mathematics, Samarkand State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On interpolation in Lp-spaces2003In: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 74, no 5, p. 782-786Article in journal (Refereed)
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  • 7.
    Astashkin, Sergei V.
    et al.
    Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sukhanov, R.S.
    Samara State University.
    Sequences of independent Walsh functions in BMO2013In: Siberian mathematical journal, ISSN 0037-4466, E-ISSN 1573-9260, Vol. 54, no 2, p. 205-211Article in journal (Refereed)
    Abstract [en]

    Under examination are the sequences of independent Walsh functions in the space of functions of bounded mean oscillation. We study geometric properties of the subspaces spanned by the sequences; in particular, some necessary and sufficient conditions are found for such a subspace to be complemented

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  • 8.
    Astashkin, Sergey
    et al.
    Samara State Univ, Dept Math & Mech, , Samara, Russia.Samara State Aerosp Univ, Samara , Russia .
    Lesnik, Karol
    Poznan Univ Tech, Inst Math, Poznan, Poland.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Isomorphic structure of Cesàro and Tandori spaces2019In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-4279, Vol. 71, no 3, p. 501-532Article in journal (Refereed)
    Abstract [en]

    We investigate the isomorphic structure of the Cesàro spaces and their duals, the Tandori spaces. The main result states that the Cesàro function space Ces∞ and its sequence counterpart ces∞ are isomorphic. This is rather surprising since Ces∞ (like Talagrand’s example) has no natural lattice predual. We prove that ces∞ is not isomorphic to ℓ∞ nor is Ces∞ isomorphic to the Tandori space L1 with the norm ∥f∥L1 = ∥f∥L1, where f(t) = esssups≥tf(s). Our investigation also involves an examination of the Schur and Dunford–Pettis properties of Cesàro and Tandori spaces. In particular, using results of Bourgain we show that a wide class of Cesàro–Marcinkiewicz and Cesàro–Lorentz spaces have the latter property.

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  • 9. Astashkin, Sergey
    et al.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Cesaro function spaces fail the fixed point property2008In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 12, p. 4289-4294Article in journal (Refereed)
    Abstract [en]

    The Cesaro sequence spaces ces(p), 1 < p < infinity, are reflexive but they have the fixed point property. In this paper we prove that in contrast to these sequence spaces the corresponding Cesaro function spaces Ces(p) on both [0, 1] and [0, infinity) for 1 < p < infinity are not reflexive and they fail to have the fixed point property.

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  • 10. Astashkin, Sergey
    et al.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Interpolation between L1 and Lp, 12004In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 10, p. 2929-2938Article in journal (Refereed)
    Abstract [en]

    The main result of this paper is that if $X$ is an interpolation rearrangement invariant space on $[0,1]$ between $L_1$ and $L_\infty$, for which the Boyd index $\alpha(X)>1/p$, $1

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  • 11. Astashkin, Sergey
    et al.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Rademacher functions in Cesaro type spaces2010In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 198, no 3, p. 235-247Article in journal (Refereed)
    Abstract [en]

    The Rademacher sums are investigated in the Cesaro spaces Ces(p) (1 <= p <= infinity) and in the weighted Korenblyum-Krein-Levin spaces K-p,K-w on [0,1]. They span l(2) space in Ces(p) for any 1 <= p < infinity and in K-p,K-w if and only if the weight w is larger than t log(2)(p/2)(2/t) on (0,1). Moreover, the span of the Rademachers is not complemented in Ces(p) for any 1 <= p < infinity or in K-1,K-w for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l(2), this span is a complemented subspace in K-p,K-w.

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  • 12. Astashkin, Sergey
    et al.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Structure of Cesaro function spaces2009In: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 20, no 3, p. 329-379Article in journal (Refereed)
    Abstract [en]

    The structure of the Cesàro function spaces Cesp on both [0,1] and [0, ∞) for 1 < p ≤ ∞ is investigated. We find their dual spaces, which equivalent norms have different description on [0, 1] and [0, ∞).The spaces Cesp for 1 < p < ∞ are not reflexive but strictly convex. They are not isomorphic to any Lq space with 1 ≤ q ≤ ∞. They have "near zero" complemented subspaces isomorphic to lp and "in the middle" contain an asymptotically isometric copy of l1 and also a copy of L1[0, 1]. They do not have Dunford-Pettis property but they do have the weak Banach-Saks property. Cesàro function spaces on [0, 1] and [0, ∞) are isomorphic for 1 < p ≤ ∞. Moreover, we give characterizations in terms of p and q when Cesp[0, 1] contains an isomorphic copy of lq.

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  • 13. Astashkin, Sergey
    et al.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ultrasymmetric Orlicz spaces2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 347, no 1, p. 273-285Article in journal (Refereed)
    Abstract [en]

    It is proved that ultrasymmetric reflexive Orlicz spaces can be described exactly as all those Orlicz spaces which can be written as some Lorentz spaces. This description is an answer to the problem posed by Pustylnik in [E. Pustylnik, Ultrasymmetric spaces, J. London Math. Soc. (2) 68 (1) (2003) 165-182]. On the other hand, the Lorentz-Orlicz spaces with non-trivial indices of their fundamental functions are ultrasymmetric.

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  • 14. Astashkin, Sergey
    et al.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Semenov, E.M.
    Department of Mathematics, Voronezh State University.
    О дополняемости подпространств,порожденных сжатиями и сдвигами функций: [On the complementness of subspaces generated by contractions and shifts of functions]2002In: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 387, no 5, p. 583-585Article in journal (Refereed)
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  • 15.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    A short proof of some recent results related to Cesàro function spaces2013In: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 24, no 3, p. 589-592Article in journal (Refereed)
    Abstract [en]

    We give a short proof of the recent results that, for every 1≤p<∞, the Cesàro function space Cesp(I) is not a dual space, has the weak Banach–Saks property and does not have the Radon–Nikodym property.

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  • 16.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Akad. Pavlova 1, 443011 Samara, Russia.
    Leibov, Mikhail
    Horton Point LLC, 1180 Avenue of the Americas, New York, U.S.A.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Rademacher functions in BMO2011In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 205, no 1, p. 83-100Article in journal (Refereed)
    Abstract [en]

    The Rademacher sums are investigated in the BMO space on [0,1]. They span an uncomplemented subspace, in contrast to the dyadic BMOd space on [0,1], where they span a complemented subspace isomorphic to l2. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in BMO are studied and an analog of the Kadec–Pełczyński type alternative with l2 and c0 spaces is proved.

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  • 17.
    Astashkin, Sergey V.
    et al.
    Samara State University, Volga, Russia.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Geometry of Cesaro function spaces2011In: Functional analysis and its applications, ISSN 0016-2663, E-ISSN 1573-8485, Vol. 45, no 1, p. 64-68Article in journal (Refereed)
    Abstract [en]

    Geometric properties of Cesàro function spaces Ces p (I), where I = [0,∞) or I = [0, 1], are investigated. In both cases, a description of their dual spaces for 1 < p < ∞ is given. We find the type and the cotype of Cesàro spaces and present a complete characterization of the spaces l q that have isomorphic copies in Ces p [0, 1] (1 ⩽ p < ∞).

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    Original paper in russian
  • 18.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Interpolation of Cesaro and Copson spaces2014In: Proceedings of the Fourth International Symposium on Banach and Function Spaces IV (ISBFS 2012): Kyushu Institute of Technology, Kitakyushu, Japan, 12-15 September 2012 / [ed] Mikio Kato; Lech Maligranda; Tomonari Suzuki, Yokohama: Yokohama Publishers, 2014, p. 123-133Conference paper (Refereed)
    Abstract [en]

    Summary. Interpolation properties of Cesàro and Copson spaces are investigated. It is shown that the Cesàro function space Ces_p(I), where I = [0, 1] or [0, \infty), is an interpolation space between Ces_{p_0}(I) and Ces_{p_1}(I) for 1 < p_0 < p_1 \leq \infty and 1/p = (1 - \theta)/p_0 + \theta /p_1 with 0 < \theta < 1. The same result is true for Cesàro sequence spaces. For Copson function and sequence spaces a similar result holds even in the case when 1 \leq p_0 < p_1 \leq \infty. At the same time, $Ces_p[0, 1]$ is not an interpolation space between Ces_1[0, 1] and Ces_{\infty}[0, 1] for any 1<p<\infty.

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  • 19.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Interpolation of cesàro sequence and function spaces2013In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 215, no 1, p. 39-69Article in journal (Refereed)
    Abstract [en]

    The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that Cesp(I) is an interpolation space between Cesp0 (I) and Cesp1 (I) for 1 < p0 < p1 ≤ ∞ and 1/p = (1 - θ)/p0 + θ/p1 with 0 < θ < 1, where I = [0,∞) or [0, 1]. The same result is true for Cesàro sequence spaces. On the other hand, Cesp[0; 1] is not an interpolation space between Ces 1[0; 1] and Ces∞[0; 1].

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  • 20.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia .
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lp + L and Lp n L are not Isomorphic for all 1 ≤ p < ∞, p ≠ 22018In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, no 5, p. 2181-2194Article in journal (Refereed)
    Abstract [en]

    We prove the result stated in the title. It comes as a consequence of the fact that the space Lp n L∞, 1 = p < ∞, p ≠ 2, does not contain a complemented subspace isomorphic to Lp. In particular, as a subproduct, we show that Lp nL∞ contains a complemented subspace isomorphic to l2 if and only if p = 2.

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  • 21.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia .
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q2018In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 356, no 6, p. 661-665Article in journal (Refereed)
    Abstract [en]

    We prove that if 1≤p,q≤∞1≤p,q≤∞, then the spaces Lp+LqLp+Lq and Lp∩LqLp∩Lq are isomorphic if and only if p=qp=q. In particular, L2+LL2+L∞ and L2∩LL2∩L∞ are not isomorphic, which is an answer to a question formulated in [2].

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  • 22.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Rademacher functions in Morrey spaces2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 444, no 2, p. 1133-1154Article in journal (Refereed)
    Abstract [en]

    The Rademacher sums are investigated in the Morrey spaces Mp,wMp,w on [0,1][0,1] for 1≤p<∞1≤p<∞ and weight w being a quasi-concave function. They span l2l2 space in Mp,wMp,w if and only if the weight w is smaller than View the MathML sourcelog2−1/2⁡2t on (0,1)(0,1). Moreover, if 1<p<∞1<p<∞ the Rademacher subspace Rp,wRp,w is complemented in Mp,wMp,w if and only if it is isomorphic to l2l2. However, the Rademacher subspace R1,wR1,w is not complemented in M1,wM1,w for any quasi-concave weight w . In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces Mp,wMp,w is described. It turns out that for any infinite-dimensional subspace X of Rp,wRp,w the following alternative holds: either X is isomorphic to l2l2 or X contains a subspace which is isomorphic to c0c0 and is complemented in Rp,wRp,w.

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  • 23.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Structure of Cesaro function spaces: a survey2014In: Banach Center Publications, ISSN 0137-6934, E-ISSN 1730-6299, Vol. 102, p. 13-40Article in journal (Refereed)
    Abstract [en]

    Summary. Geometric structure of Cesàro function spaces Ces_p(I), where I = [0, 1] and [0,\infty), is investigated. Among other matters we present a description of their dual spaces, characterize the sets of all q such that Ces_p[0, 1] contains isomorphic and complemented copies of lq-spaces, show that Cesàro function spaces fail the fixed point property, give a description of subspaces generated by Rademacher functions in spaces Ces_p[0, 1].

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  • 24.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Structure of Rademacher subspaces in Cesàro type spaces2015In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 226, no 3, p. 259-279Article in journal (Refereed)
    Abstract [en]

    The structure of the closed linear span R of the Rademacher functions in the Cesàro space Ces∞ is investigated. It is shown that every infinite-dimensional subspace of R either is isomorphic to l2 and uncomplemented in Ces∞, or contains a subspace isomorphic to c0 and complemented in R. The situation is rather different in the p-convexification of Ces∞ if 1 < p < ∞.

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  • 25. Astashkin, Sergey V.
    et al.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Semenov, E. M.
    Department of Mathematics, Voronezh State University.
    Multiplicator space and complemented subspaces of rearrangement invariant space2003In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 202, no 1, p. 247-276Article in journal (Refereed)
    Abstract [en]

    We show that the multiplicator space M(X) of an rearrangement invariant (r.i.) space X on [0, 1] and the nice part N0 (X) of X, that is, the set of all a ∈ X for which the subspaces generated by sequences of dilations and translations of a are uniformly complemented, coincide when the space X is separable. In the general case, the nice part is larger than the multiplicator space. Several examples of descriptions of M(X) and N0(X) for concrete X are presented

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  • 26.
    Astashkin, Sergey V.
    et al.
    Department of Mathematics and Mechanics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Tikhomirov, Konstantin E.
    Department of Mathematical and Statistical Sciences, University of Alberta.
    New examples of K-monotone weighted Banach couples2013In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 218, no 1, p. 55-88Article in journal (Refereed)
    Abstract [en]

    Some new examples of K-monotone couples of the type (X;X(ω)), where X is a symmetric space on [0; 1] and ω is a weight on [0; 1], are presented. Based on the property of ω-decomposability of a symmetric space we show that, if a weight ω changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X;X(ω)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t1/p for some p ⋯ [1;∞], then X = Lp. At the same time a Banach couple (X;X(ω)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space, we find conditions which guarantee that (X;X(ω)) is K-monotone

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  • 27.
    Astashkin, S.V.
    et al.
    Department of Mathematics, Samara State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Semenov, E.M.
    Department of Mathematics, Voronezh State University.
    On complementability of subspaces generated by contractions and shifts of functions2002In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 66, no 3, p. 390-392Article in journal (Refereed)
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  • 28.
    Balińska, Marta Aleksandra
    et al.
    Department of Public Health Centre, Hospitalier Universitaire de Nice, Nice, France.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Poznań University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, Poland.
    A photo of the mathematician Aleksander Rajchman has finally been found: [W końcu odnaleziono zdjęcie matematykaAleksandra Rajchmana]2022In: Antiquitates Mathematicae, ISSN 1898-5203, E-ISSN 2353-8813, Vol. 16, no 1, p. 181-187Article in journal (Refereed)
    Abstract [en]

    Aleksander Michał Rajchman (1890-1940) was a Polish mathematician and had a great influence on the development of mathematical analysis. For a long time there was no known picture of him available, but we have recently relocated one which we wish to share with other mathematicians.

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  • 29.
    Berezhnoi, E. I.
    et al.
    Department of Mathematics, Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000 Russia.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Extrapolation of operators and the limits of applicability of Schur's test2003In: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 393, no 5, p. 583-586Article in journal (Refereed)
    Abstract [en]

    Generalizations of the Schur test for integral operators are studied. The authors look at the test from the point of the modern theory of extrapolation of operators. The generalizations are of two types. First of all, instead of operators with positive kernel, a more general class of positive operators is considered. Moreover, instead of Lp spaces, Orlicz, Lorentz and Marcinkiewicz spaces are taken as underlying spaces. In particular it is stated that the Schur extrapolation theorem holds for the class of positive operators. Several negative results are formulated. For instance, the authors show that the Schur extrapolation theorem does not hold for the sublinear Hardy operator in the Lp scale and for the classical Hardy operator in some reflective Orlicz spaces. Moreover, it is claimed that for a certain class of operators one can use Lorentz and Marcinkiewicz spaces instead of L1.and L∞ Proofs are not given.

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  • 30.
    Berezhnoi, E. I.
    et al.
    Yaroslavl State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Representability of cones in weighted Lebesgue spaces and extrapolation operators on cones2006In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 73, no 1, p. 59-62Article in journal (Refereed)
    Abstract [en]

    Representability of cones in weighted Lebesgue spaces and extrapolation operators on cones are discussed. Estimates of operators on some cones in spaces rather than on the entire spaces have become very popular. A reduction of estimating operators on cones to estimating them on new spaces is suggested. such reduction makes it possible to apply the whole apparatus developed for obtaining exact estimates on weith Lebesgue spaces to obtain exact estimates of operators on cones. Using the reduction, it is proved that a new extrapolation theorem for a certain class of operator defined on cones in Lebesgue spaces.

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  • 31.
    Berezhnoi, Evgeni
    et al.
    Yaroslav State Univerity, Yaroslavl, Russia.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On the representability of cones of monotone functions in weighted Lebesgue spaces and the extrapolation of operators on these cones2017In: Algebra i Analiz, ISSN 0234-0852, Vol. 29, no 4, p. 1-44Article in journal (Refereed)
    Abstract [en]

    We have proved that boundedness of a sublinear operator on the cone of monotone functions is equivalent to boundedness of the involved operator with it on a new space, which is constructively built. Using this construction we were able to prove a new extrapolation theorems on this cone in weighted Lebesgue spaces.

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  • 32.
    Berezhnoǐ, Eugenii I.
    et al.
    P. G. Demidov Yaroslavl, State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Represensibility of cones of monotone functions in weighted Lebesgue spaces and extrapolation of operators on these cones2018In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 29, no 4, p. 545-574Article in journal (Refereed)
    Abstract [en]

    It is shown that a sublinear operator is bounded on the cone of monotone functions if and only if a certain new operator related to the one mentioned above is bounded on a certain ideal space defined constructively. This construction is used to provide new extrapolation theorems for operators on the cone in weighted Lebesgue spaces.

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  • 33.
    Berezhoi, E.I.
    et al.
    Department of Mathematics, Yaroslavl State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Representability of some cones in weighted Lebesgue spaces and the extrapolation of operators on cones2006In: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 406, no 4, p. 439-442Article in journal (Refereed)
    Abstract [en]

    In this paper, for the most important cones in Lebesgue spaces, we propose reducing the problem of an estimate for an operator on a cone to the problem of an estimate for an operator on a new space, which is obtained constructively from the cone and the original space. Such a reduction makes it possible to apply the entire apparatus developed for obtaining sharp estimates on weighted Lebesgue spaces to obtain sharp estimates for operators on cones. Using this reduction, we also state, for a certain class of operators, a new theorem on the extrapolation of operators defined on cones in Lebesgue spaces.

  • 34.
    Berezhoi, Evgenii I.
    et al.
    Department of Mathematics, Yaroslavl State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Representation of Banach ideal spaces and factorization of operators2003Report (Other academic)
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  • 35.
    Berezhoi, Evgenii I.
    et al.
    Department of Mathematics, Yaroslavl State University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Representation of Banach ideal spaces and factorization of operators2005In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-4279, Vol. 57, no 5, p. 897-940Article in journal (Refereed)
    Abstract [en]

    Representation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón-Lozanovskiǐ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lp spaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far from Lp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón-Lozanovskiǐ construction are involved in the proofs

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  • 36.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3a, 60-965, Poznań, Poland.
    A new result on boundedness of the Riesz potential in central Morrey–Orlicz spaces2023In: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 27, no 5, article id 62Article in journal (Refereed)
    Abstract [en]

    We improve our results on boundedness of the Riesz potential in the central Morrey–Orlicz spaces and the corresponding weak-type version. We also present two new properties of the central Morrey–Orlicz spaces: nontriviality and inclusion property.

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  • 37.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3a, 60-965 Poznan, Poland.
    Matsuoka, Katsuo
    College of Economics, Nihon University, 1-3-2 Misaki-cho, Kanda, Chiyoda-ku, Tokyo 101-8360, Japan.
    Boundedness of the Riesz potential in central Morrey-Orlicz spaces2022In: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 26, no 1, article id 22Article in journal (Refereed)
    Abstract [en]

    Boundedness of the maximal operator and the Calderón–Zygmund singular integral operators in central Morrey–Orlicz spaces were proved in papers (Maligranda et al. in Colloq Math 138:165–181, 2015; Maligranda et al. in Tohoku Math J 72:235–259, 2020) by the second and third authors. The weak-type estimates have also been proven. Here we show boundedness of the Riesz potential in central Morrey–Orlicz spaces and the corresponding weak-type version. 

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  • 38.
    Ciesielska, Danuta
    et al.
    Instytut Matematyki, Uniwersytet Pedagogiczny w Krakowie, Krakow, Poland.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Alfred Rosenblatt (1880-1947)2014In: Wiadomosci Matematyczne, ISSN 2080-5519, Vol. 50, no 2, p. 221-259Article in journal (Refereed)
    Abstract [en]

    Summary. Life of Alfred Rosenblatt (1880-1947) is precisely discribed. We tried to bring the Polish reader forgotten figure of the Krakow mathematics. We have gathered all the information related to his life, his work and achievements in mathematics and in applications of mathematics. We greached also written information about it in Spanish. Rosenblatt has published almostthree hundred scientific papers in many areas of mathematics and its applications. In addition, he participated in four International Congresses of Mathematicians in Cambridge (1912), Strasbourg (1920), Bologna (1928) and Zurich (1932). Streszczenie. Zycie Alfreda Rosenblatta (1880-1947) zostało dokładnie opisane. Staralismy sie przyblizyc polskiemu czytelnikowi sylwetke tego zapomnianego krakowskiego matematyka.Zebralismy wszelkie informacje zwiazane z jego zyciem, jego pracami i osiagnieciami wmatematyce oraz w zastosowaniach matematyki. Dotarlismy rowniez do informacji pisanych o nim po hiszpansku. Rosenblatt opublikowal prawie trzysta prac naukowych w wieludziedzinach matematyki i jej zastosowan. Ponadto uczestniczyl w czterech Miedzynarodowych Kongresach Matematykow w Cambridge (1912), Strasburgu (1920), Bolonii (1928) i Zurichu (1932).

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  • 39.
    Ciesielska, Danuta
    et al.
    Ludwik and Aleksander Birkenmajer Institute for the History of Science, Polish Academy of Sciences, ul. Nowy Świat 72, 00-330 Warsaw, Poland.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Alfred Rosenblatt (1880-1947). Polish-Peruvian mathematician2019In: Banach Center Publications, ISSN 0137-6934, E-ISSN 1730-6299, Vol. 119, p. 57-108Article in journal (Refereed)
    Abstract [en]

    Alfred Rosenblatt (1880-1947) was a Polish mathematician born into a Jewish family in Krakow (Kraków, Poland). He studied in Vienna, Krakow, Göttingen, and worked at the Jagiellonian University in Krakow (1910-1936) and at the University of San Marcos in Lima, Peru (1936-1947). During the Second World War, Rosenblatt accepted Peruvian citizenship. His work was important for the development of mathematics in Peru, including the foundation of the National Academy of Exact Sciences, Physics and Natural Sciences in Lima. He is mentioned among the four mathematicians of the twentieth century most important for Peru (F. Villarreal, G. Garcia Diaz, A. Rosenblatt and J. Tola Pasquel). He spent the first half of 1947 on a scholarship at the Institute for Advanced Study in Princeton and had several lectures at other universities in the USA.

    Rosenblatt published almost three hundred scientific papers in various fields of pure and applied mathematics, including ordinary and partial differential equations, algebraic geometry, theory of analytic functions, probability, mathematical physics, three-body problem, hydrodynamics and other applications of mathematics. About 180 papers were published in the years of his work in Poland and about 120 in the years he worked in Peru. His publications are in Polish, German, French, Italian, Spanish and English. Rosenblatt participated actively in four International Congresses of Mathematicians: Cambridge (1912), Strasbourg (1920), Bologna (1928), Zurich (1932). He presented three talks in Bologna and one in Zurich.

    We describe Alfred Rosenblatt's life and important parts of his work in detail. We have made an effort to see all his papers, so as not to miss any of his achievements in mathematics and applications, including papers and information written in Spanish; e.g., [Ro11], [Ro13]-[Ro16] and [Ro20]. We have already written three articles, two in Polish [Ro8], [Ro9] and one in Russian [Ro12], to introduce him to Polish and Russian mathematicians. Now we want to do the same for a wider range of scientists with this article in English. Some information on Rosenblatt can also be found in [Ro1]-[Ro6], [Ro10] and [Ro17]-[Ro19].

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  • 40.
    Ciesielska, Danuta
    et al.
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie Instytut Matematyki, ul. Podchorążych 2, 30-084 Kraków, Poland.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Alfred Rosenblatt (1880-1947). Publikacje, odczyty i wyklady2014In: Antiquitates Mathematicae, ISSN 1898-5203, Vol. 8, no 1, p. 3-45Article in journal (Refereed)
    Abstract [en]

    The aim of the paper is to present scientific and educationalachievements of Alfred Rosenblatt (1880-1947). We have collected thefirst complete list of scientific papers and books by Rosenblatt. Thelist is divided into the following parts: textbooks and monographs, scientificarticles in the field of mathematics and its applications, astronomy,history of mathematics and reviews, translations and other. Frompublished and unpublished sources we collected information about hislectures and short presentations on conferences, among others on InternationalCongresses of Mathematicians, Congresses of Mathematiciansof Slavic Countries, Polish Mathematical Society Meetings and others.Complete list of Rosenblatt’s academic lectures at the Jagiellonian Universityand available information about lectures at the National Universityof San Marcos in Lima are collected. A very short biographyof Rosenblatt and overview of his scientific results in algebraic geometry,differential equations, analytic function, calculus of variations,probability theory and statistics, and application of mathematics inhydrodynamic is presented.Streszczenie Celem artykułu jest zaprezentowanie dorobku naukowegoi dydaktycznego Alfreda Rosenblatta (1880-1947). Zgromadzilsmypierwszy kompletny spis jego artykułów i ksiazek naukowych,z podziałem na: podreczniki i monografie, artykuły naukowe z zakresumatematyki i jej zastosowan, astronomii, historii matematyki w tymbiografie oraz recenzje, tłumaczenia i inne. Zebralismy w publikowanychi niepublikowanych zródłach informacje o jego odczytach, w tymo odczytach i komunikatach na Miedzynarodowych Kongresach Matematyków,wystapieniach na Kongresach Matematyków Krajów Słowianskich,Zjazdach PTM i innych. Przedstawilismy kompletny spiswykładów Rosenblatta na Uniwersytecie Jagiellonskim oraz dostepneinformacje o wykładach na Uniwersytecie Swietego Marka w Limie. Ponadtow artykule znajduje sie krótki biogram A. Rosenblatta i krótkieomówienie jego wyników naukowych z geometrii algebraicznej, teoriirównan rózniczkowych, funkcji analitycznych, rachunku wariacyjnego,szeregów, rachunku prawdopodobienstwa i statystyki oraz zastosowanmatematyki w hydrodynamice

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  • 41.
    Ciesielska, Danuta
    et al.
    Instytut Historii Nauki PAN.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Zwierzyńska, Joanna
    Instytut Historii Nauki PAN.
    Doktoraty Polaków w Getyndze. Matematyka2019In: Analecta. Studia i materiały z dziejów nauki, ISSN 1509-0957, Vol. 28, no 2, p. 73-116Article in journal (Refereed)
    Abstract [en]

    The article provides information about the documents held in the archives of the Georg August University in Göttingen (Georg-August-Universität Göttingen), pertaining to the efforts of Poles who wanted to obtain a doctorate in mathematics. In the years 1892–1922, ten Poles were awarded doctorates in exact sciences in Göttingen, including fi ve in mathematics. Michał Feldblum from Warsaw, Hugo Steinhaus from Jasło and Arnold Walfi sz from Warsaw received doctorates in pure mathematics, Władysław Bortkiewicz from Saint Petersburg in mathematical statistics and Jan Kroo from Krakow in mathematical physics. From the documents related to these fi ve doctoral proceedings, the authors have extracted the information that has not been hitherto published, including the opinions on doctoral dissertations (by Hilbert, Landau, Lexis, and Voigt), exam questions, opinions on the results achieved by doctoral students, and handwritten CVs. The documents have been translated into Polish.

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  • 42.
    Ciesielska, Danuta
    et al.
    Instytut Historii Nauki PAN im. Ludwika i Aleksandra Birkenmajerów, Pałac Staszica w Warszawie, Warszawa, Poland.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Instytut Matematyki, Politechnika Poznańska ul. Piotrowo 3A, Poznań, Poland.
    Zwierzyńska, Joanna
    Instytut Historii Nauki PAN im. Ludwika i Aleksandra Birkenmajerów, Pałac Staszica w Warszawie, Warszawa, Poland.
    W świątyni nauki, mekce matematyków: Studia i badania naukowe polskich matematyków, fizyków i astronomów na Uniwersytecie w Getyndze 1884-19332022 (ed. 1)Book (Refereed)
    Abstract [en]

    The book is the first comprehensive one based on archival materials description of studies and research internships of Poles who matriculated on University of Göttingen in 1884-1933 and undertook studies in exact sciences. The first chapter of the work is a methodological introduction, the second chapter presents the development of exact sciences at the university in Göttingen from its foundation to the expulsion of scientists by the Nazi governments in 1933. The third chapter was devoted to general problems related to studies in Göttingen. In chapters four and five - in chronological order - presented are Poles who completed research internships at the University of Göttingen, and people who obtained a doctorate in philosophy in mathematics, mathematical statistics and physics here, or who took a doctoral exam in these disciplines. A short summary of the research is the sixth chapter discussing the role of former Gettingenian students in the Second Polish Republic in the interwar period. An important part of the publication is the penultimate chapter containing short biographies of nearly eighty Polish women who matriculated at the University of Göttingen. The biographies were supplemented with archival information collected during the inquiries in Göttingen, as well as in many Polish and foreign archives and libraries. A few notes are the first biographical information on these characters. The advantages of the monograph are rich documentation and illustrative material obtained from Polish and foreign archives. The publication is aimed primarily at academics and students interested in the history of mathematics, physics, astronomy and mathematical statistics. It may also interest people interested in the history of university education, including Polish-German scientific contacts in the period 1870-1939, and historians of philosophy, logic and chemistry.

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  • 43.
    Cui, Yunan
    et al.
    Harbin University of Science and Technology.
    Hudzik, Henryk
    Adam Mickiewicz University, Poznan.
    Kumar, Romesh
    University of Jammu.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Composition operators in Orlicz spaces2004In: Journal of the Australian Mathematical Society, ISSN 1446-7887, E-ISSN 1446-8107, Vol. 76, no 2, p. 189-206Article in journal (Refereed)
    Abstract [en]

    Composition operators Cτ between Orlicz spaces L (Ω, Σ, μ) generated by measurable and nonsingular transformations τ from Ω into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping τ, the function and the measure space (Ω, Σ, μ). These results generalize earlier results known for Lp-spaces.

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  • 44.
    Cwikel, Michael
    et al.
    Department of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel.
    Kaminsk, Anna
    Department of Mathematical Sciences, The University of Memphis, Memphis, TN, USA.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Pick, Lubos
    Department of Mathematical Analysis, Charles University, Czech Republic.
    Are generalized Lorentz "spaces" really spaces?2003Report (Other academic)
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  • 45.
    Cwikel, Michael
    et al.
    Department of Mathematics, Technion - Israel Institute of Technology.
    Kaminska, Anna
    University of Memphis.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Pick, Lubos
    Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovsk.
    Are generalized Lorentz "spaces" really spaces?2004In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 12, p. 3615-3625Article in journal (Refereed)
    Abstract [en]

    Let $w$ be a non-negative measurable function on $(0,\infty)$, non-identically zero, such that $W(t)=\int_0^tw(s)ds<\infty$ for all $t>0$. The authors study conditions on $w$ for the Lorentz spaces $\Lambda^p(w)$ and $\Lambda^{p,\infty}(w)$, defined by the conditions $\int_0^\infty (f^*(t))^pw(t)dt<\infty$ and $\sup_{00,$$ it is shown that, if $\varphi$ satisfies the $\Delta_2$-condition and $w>0$, then $\Lambda_{\varphi,w}$ is a linear space if and only if $W$ satisfies the $\Delta_2$-condition.

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  • 46.
    Echandía, Ventura
    et al.
    Department of Mathematics, Central University of Venezuela.
    Finol, Carslos E.
    Department of Mathematics, Central University of Venezuela.
    Maligranda, Lech
    Interpolation of some spaces of Orlicz type I1990In: Polish Academy of Sciences. Bulletin. Mathematics, ISSN 0239-7269, Vol. 38, no 1-2, p. 125-134Article in journal (Refereed)
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  • 47. Feher, F.
    et al.
    Maligranda, Lech
    Interpolation of some concrete symmetric spaces1985Conference paper (Refereed)
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  • 48.
    Finol, C. E.
    et al.
    Department of Mathematics, Central University of Venezuela.
    Hudzik, H.
    Faculty of Mathematics and Computer Science, Adam Mickiewicz University.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Orlicz spaces which are AM-spaces1997In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 69, no 3, p. 234-242Article in journal (Refereed)
    Abstract [en]

    The Orlicz function and sequence spaces which are AM-spaces are characterized for both the Luxemburg-Nakano and the Amemiya (Orlicz) norm.

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  • 49.
    Finol, Carlos E.
    et al.
    Department of Mathematics, Central University of Venezuela.
    Maligranda, Lech
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Reiteration for and exact relations between some real interpolation spaces1991In: Function spaces: Proceedings of the 2nd international conference, Poznan, Poland, August 28-September 2, 1989 / [ed] Julian Musielak; Henry Hudzik; Ryszard Urbanski, Stuttgart: Teubner , 1991, p. 238-247Conference paper (Refereed)
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  • 50.
    Finol, C.E.
    et al.
    Department of Mathematics, Central University of Venezuela.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On a decomposition of some functions1991In: Annales Societatis Mathematicae Polonae. Series 1: Commentationes Mathematicae - Prace Matematyczne, ISSN 0373-8299, Vol. 30, no 2, p. 285-291Article in journal (Refereed)
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