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  • 101.
    Gogatishvili, Amiram
    et al.
    Mathematical Institute, Academy Sciences of the Czesh Republic.
    Kufner, Alois
    Mathematical Institute, Academy Sciences of the Czesh Republic.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    An equivalence theorem for integral conditions related to Hardy's inequality2003In: Real Analysis Exchange, ISSN 0147-1937, E-ISSN 1930-1219, Vol. 29, no 2, p. 867-880Article in journal (Refereed)
  • 102.
    Gogatishvili, Amiran
    et al.
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Kufner, Alois
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Weighted Stieltjes inequality and applications2013In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 286, no 7, p. 659-668Article in journal (Refereed)
    Abstract [en]

    Let 1 < p ≤ q < ∞. Inspired by some results concerning characterization of weighted Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the Stieltjes transform. By applying our result to weighted inequalities for the Stieltjes transform we obtain four new scales of conditions for characterization of this inequality. We also derive a new characterization for the solvability of a Riccati type equation and show via our new results that this characterization can be done in infinite many ways via our four scales of equivalent conditions.

  • 103.
    Gogatishvili, Amiran
    et al.
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir D.
    Department of Mathematical Analysis, Russian Peoples' Friendship University.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some scales of equivalent conditions to characterize the Stieltjes inequality: the case q2014In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 287, no 2-3, p. 242-253Article in journal (Refereed)
    Abstract [en]

    We prove that the weighted Stieltjes inequality can be characterized by four different scales of conditions also for the case , . In particular, a new proof of a result of G. Sinnamon is given, which also covers the case . Moreover, for the situation at hand a new gluing theorem and also an equivalence theorem of independent interest are proved and discussed. By applying our new equivalence theorem to weighted inequalities for the Stieltjes transform we obtain the four new scales of conditions for characterization of Stieltjes inequality

  • 104.
    Gogatishvili, Amiran
    et al.
    Mathematical Institute, Czech Academy of Sciences.
    Johansson, Maria
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Okpoti, Christopher
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Characterisation of embeddings in Lorentz spaces2007In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 76, no 1, p. 69-92Article in journal (Refereed)
    Abstract [en]

    Some new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embeddingSome new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embedding

  • 105.
    Gogatishvili, Amiran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Kufner, Alois
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    An equivalence theorem with application to Hardy's inequality2007Report (Other academic)
  • 106. Gogatishvili, Amiran
    et al.
    Kufner, Alois
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new scales of characterization of Hardy's inequality2010In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, no 1, p. 7-18Article in journal (Refereed)
    Abstract [en]

    Let 1 < p ≤ q < ∞. Inspired by some recent results concerning Hardy-type inequalities where the equivalence of four scales of integral conditions was proved, we use related ideas to find ten new equivalence scales of integral conditions. By applying this result to the original Hardy-type inequality, we obtain a new proof of a number of characterizations of the Hardy inequality and also some new weight characterizations.

  • 107.
    Gogatishvili, Amiran
    et al.
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Kufner, Alois
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new scales of weight characterizations of the class Bp2009In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 123, no 4, p. 365-377Article in journal (Refereed)
    Abstract [en]

    We present an equivalence theorem, which includes all known characterizations of the class B p , i.e., the weight class of Ariño and Muckenhoupt, and also some new equivalent characterizations. We also give equivalent characterizations for the classes B p *, B ∞ * and RB p , and prove and apply a "gluing lemma" of independent interest.

  • 108.
    Gogatishvili, Amiran
    et al.
    Mathematical Institute, Czech Academy of Sciences.
    Kufner, Alois
    Mathematical Institute, Czech Academy of Sciences.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Compactness of the Hardy operator and its limiting case2006In: Soochow Journal of Mathematics, ISSN 0250-3255, Vol. 32, no 1, p. 21-35Article in journal (Refereed)
    Abstract [en]

    Let 1 < p q < 1: Inspired by some recent results concerning Hardy type inequalities where the equivalence of four scales of integral conditions is proved, we use related ideas to prove some new compactness results for the Hardy operator, and we give the corresponding scales for the Polya-Knopp inequality.

  • 109.
    Gogatishvili, Amiran
    et al.
    Institute of Mathematics, Academy of Sciences of Czech Republic.
    Mustafayev, Rza
    Department of Mathematics, Faculty of Science and Arts, Kirikkale University.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new iterated Hardy-type inequalities: The case θ=12013In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, article id 515Article in journal (Refereed)
    Abstract [en]

    In this paper we characterize the validity of the Hardy-type inequality parallel to parallel to integral(infinity)(s)h(z)dz parallel to(p,u,(0,t))parallel to(q,w,(0,infinity)) <= c parallel to h parallel to(1,v,(0,infinity)), where 0 < p < infinity, 0 < q <= +infinity, u, w and v are weight functions on (0, infinity). It is pointed out that this characterization can be used to obtain new characterizations for the boundedness between weighted Lebesgue spaces for Hardy-type operators restricted to the cone of monotone functions and for the generalized Stieltjes operator.

  • 110.
    Gogatishvili, Amiran
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On scales of equivalent conditions characterizing weighted Stieltjes inequality2012In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 86, no 3, p. 738-739Article in journal (Refereed)
  • 111.
    Gogatishvili, Amiran S.
    et al.
    Institute of Mathematics, Academy of Sciences of Czech Republic.
    Mustafayev, Rza Ch
    Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new iterated Hardy-type inequalities2012In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965Article in journal (Refereed)
    Abstract [en]

    We characterize the validity of the Hardy-type inequality ∫ s ∞ h (z) d z p, u, (0, t)q, w, (0, ∞) ≤ c h θ, v (0, ∞), where 0 < p < ∞, 0 < q ≤ ∞, 1 < θ ≤ ∞, u, w, and v are weight functions on (0, ∞). Some fairly new discretizing and antidiscretizing techniques of independent interest are used.

  • 112. Grevholm, Barbro
    et al.
    Lundqvist, Josefin
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ett mentorprojekt för gymnasieelever i Luleå2012In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 2012, no 2, p. 33-37Article in journal (Other (popular science, discussion, etc.))
  • 113.
    Grevholm, Barbro
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    A dynamic model for education of doctoral students and guidance of supervisors in research groups2005In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 60, no 2, p. 173-197Article in journal (Refereed)
    Abstract [en]

    In the department of mathematics of the Luleå University of Technology in Sweden, a dynamic model for the education of doctoral students and guidance of supervisors in research groups has been developed and applied for several years now. Presently groups in mathematics as well as a group in mathematics education are working according to this model and treated in the same way. Moreover, both the students and the supervisors get some education and experience also in elements, which usually are not included in more traditional models for supervision in the mathematical sciences in Sweden. In this paper, we describe our model as well as some experiences of it. Moreover, the results of a questionnaire addressed to and answered by all doctoral students (both finished and still in the program) are presented, evaluated and compared with some related investigations in Sweden. We claim that the students in general are very satisfied to be supervised and guided in this way. In principle, there have been no cases of dropping out of the Ph.D. programs, students obtained their degrees within the stipulated time and the careers after the studies have been successful. We hope that this positive experience will stimulate other universities to test and evaluate our model (or relevant parts of it) under different conditions.

  • 114.
    Grevholm, Barbro
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    En dynamisk modell för handledning av doktorander och handledare i forskargrupper2004In: Den första nordiska forskarhandledarkonferensen: 13-15 maj 2003 i Umeå, Umeå universitet , 2004, p. 37-68Conference paper (Refereed)
  • 115.
    Gupta, Babita
    et al.
    Department of Mathematics, University of Delhi.
    Jain, Pankaj
    Department of Mathematics, University of Delhi.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Weighted geometric mean inequalities over cones in Rn2003In: Journal of Inequalities in Pure and Applied Mathematics, ISSN 1443-5756, E-ISSN 1443-5756, Vol. 4, no 4, article id 68Article in journal (Refereed)
  • 116.
    Gyllenberg, Mats
    et al.
    Luleå tekniska universitet.
    Persson, Lars-ErikLuleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Analysis, algebra, and computers in mathematical research: proceedings of the twenty-first Nordic Congress of Mathematicians1994Collection (editor) (Other academic)
  • 117.
    Hansen, Frank
    et al.
    Department of Economics, Copenhagen University.
    Krulić, Kristina
    Faculty of Textile Technology, University of Zagreb.
    Pečarić, Josip
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Generalized noncommutative Hardy and Hardy-Hilbert type inequalities2010In: International Journal of Mathematics, ISSN 0129-167X, Vol. 21, no 10, p. 1283-1295Article in journal (Refereed)
    Abstract [en]

    We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.

  • 118.
    Heinig, Hans
    et al.
    Department of Mathematics, McMaster University.
    Kufner, Alois
    Mathematical Institute, Czech Academy of Sciences.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some generalisations and refinements of the Hardy inequality1998In: Recent progress in inequalities, Dordrecht: Kluwer Academic Publishers, 1998, p. 271-288Chapter in book (Other academic)
  • 119.
    Heinig, Hans P.
    et al.
    Department of Mathematics and Statistics, McMaster University, Hamilton.
    Kufner, Alois
    Mathematical Institute, Czech Academy of Sciences.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On some fractional order Hardy inequalities1997In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 1, no 1, p. 25-46Article in journal (Refereed)
    Abstract [en]

    Weighted inequalities for fractional derivatives (= fractional order Hardy-type inequalities) have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.

  • 120.
    Helsing, Johan
    et al.
    Kungliga tekniska högskolan, KTH.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wall, Peter
    Numerical and mathematical methods for calculations of effective properties of multiphase materials1997In: Proceedings of the Fourth International Conference on Composites Engineering: ICCE/4 / [ed] David Hui, 1997, p. 855-856Conference paper (Refereed)
  • 121.
    Holmbom, Anders
    et al.
    Department of Mathematics, Ostersund University.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Svanstedt, Nils
    Luleå tekniska universitet.
    A homogenization procedure for computing effective moduli and microstresses in elastic composite materials1992In: Composites Engineering, ISSN 0961-9526, Vol. 2, no 4, p. 249-259Article in journal (Refereed)
    Abstract [en]

    Effective properties and microstress variations of elastic fiber composites are studied by means of the homogenization method. Some numerical results are obtained by using the finite element code HOMO. The model problem is a two-phase elastic fiber composite consisting of boron fibers in an epoxy matrix with various fractions of the two phases. The homogenized stiffness matrices are compared with the weighted harmonic and arithmetic means, respectively.

  • 122.
    Hudzik, Henryk
    et al.
    Adam Mickiewicz University, Poznan.
    Mastylo, Mieczyslaw
    Adam Mickiewicz University, Poznan.
    Maligranda, Lech
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Extension of submultiplicativity and supermultiplicativity of Orlicz functions1999In: Real Analysis Exchange, ISSN 0147-1937, E-ISSN 1930-1219, Vol. 24, no 2, p. 567-578Article in journal (Refereed)
  • 123.
    Høibakk, Ralph
    et al.
    UiT The Arctic University of Norway.
    Lukkassen, Dag
    UiT The Arctic University of Norway.
    Meidell, Annette
    UiT The Arctic University of Norway.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT The Arctic University of Norway.
    On some power means and their geometric constructions2018In: Mathematica Æterna, ISSN 1314-3336, E-ISSN 1314-3344, Vol. 8, no 3, p. 139-158Article in journal (Refereed)
    Abstract [en]

    The main aim of this paper is to further develop the recently initiatedresearch concerning geometric construction of some power means wherethe variables are appearing as line segments. It will be demonstratedthat the arithmetic mean, the harmonic mean and the quadratic meancan be constructed for any number of variables and that all power meanswhere the number of variables are n = 2m, m 1 2 N for all powersk = 2􀀀q and k = 2q; q 2 N can be geometrically constructed.

  • 124.
    Iqbal, Sajid
    et al.
    Department of Mathematics, University of Sargodha (Sub-Campus Mianwali), Mianwali, Pakistan.
    Pečarić, Josip
    Faculty of Textile Technology, University of Zagreb, Croatia.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UIT The Artic University of Norway.
    Tomovski, Zivorad
    aculty of Mathematics and Natural Sciences, Macedonia.
    Weighted Hardy-type inequalities involving convex function for fractional calculus operators2018In: Transactions of A. Razmadze Mathematical Institute, ISSN 2346-8092, Vol. 172, no 2, p. 205-222Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to establish some new weighted Hardy-type inequalities involving convex and monotone convex functions using Hilfer fractional derivative and fractional integral operator with generalized Mittag-Leffler function in its kernel. We also discuss one dimensional cases of our related results. As a special case of our general results we obtain the results of Iqbal et al. (2017). Moreover, the refinement of Hardy-type inequalities for Hilfer fractional derivative is also included.

  • 125.
    Isac, George
    et al.
    Department of Mathematics and Computer Science, Royal Military College of Canada.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Inequalities related to isotonicity of projection and antiprojection operators1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 1, p. 85-97Article in journal (Refereed)
    Abstract [en]

    The metric projection operator is an important tool in numerical analysis, optimization, variational inequalities and complementarity problems and has been considered from the point of view of isotonicity, with respect to an ordering compatible with the vector structure on Hilbert spaces and Banach spaces. In this paper, the authors study some inequalities related to the isotonicity of the metric projection operator onto a closed convex set in an ordered Banach space. The concept of antiprojection operator onto a compact nonempty subset of a Hilbert space is introduced and the relationship between the new inequality obtained by the authors and the isotonicity of such an operator is also discussed.

  • 126.
    Isac, George
    et al.
    Department of Mathematics, Royal Military College, Kingston, Ontario.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On an inequality related to the isotonicity of the projection operator1996In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 86, no 2, p. 129-143Article in journal (Refereed)
    Abstract [en]

    In connection to the study of the isotonicity of the projection operator onto a closed convex set in an ordered Hilbert space, Isac has recently remarked the importance of an inequality named "the property of four elements" (PFE). In this paper a sharp inequality closely connected to (PFE) is proved in a Banach space setting. The property (PFE)Vfor Lyapunov functionalsVis introduced and studied. Some applications are included.

  • 127.
    Jain, Pankaj
    et al.
    Department of Mathematics, University of Delhi.
    Lukkassen, Dag
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Svanstedt, Nils
    Chalmers University of Technology, Department of Mathematics.
    Imbeddings of anisotropic Orlicz-Sobolev spaces and applications2002In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 5, no 2, p. 181-195Article in journal (Refereed)
  • 128.
    Jain, Pankaj
    et al.
    Department of Mathematics, University of Delhi.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Remarks on recent results of Oguntuase and Imoru2001In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 255, no 1, p. 105-108Article in journal (Refereed)
  • 129.
    Jain, Pankaj
    et al.
    University of Delhi, Department of Mathematics, Deshbandhu College.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Upreti, P.
    University of Delhi, Motilal Nehru College, Department of Mathematics, New Delhi.
    Inequalities and properties of some generalized Orlicz classes and spaces2007In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 117, no 1-2, p. 161-174Article in journal (Refereed)
    Abstract [en]

    We discuss and complement the knowledge about generalized Orlicz classes X-Phi and Orlicz spaces X-Phi obtained by replacing the space L-1 in the classical construction by an arbitrary Banach function space X. Our main aim is to focus on the task to study inequalities in such spaces. We prove a number of new inequalities and also natural generalizations of some classical ones (e.g., Minkowski's, Holder's and Young's inequalities). Moreover, a number of other basic facts for further study of inequalities and function spaces are included.

  • 130.
    Jain, Pankaj
    et al.
    University of Delhi, Department of Mathematics, Deshbandhu College.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Upreti, Priti
    University of Delhi, Motilal Nehru College, Department of Mathematics, New Delhi.
    On products of generalized Orlicz spaces2012In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 15, no 3, p. 663-674Article in journal (Refereed)
    Abstract [en]

    In the context of generalized Orlicz spaces, the products X-Phi 1 circle dot X-Phi 2 and X-Phi 1 circle times X-Phi 2 are studied and conditions are obtained under which these spaces are contained in a suitable space X-Phi. These imbedding results (inequalities) are in a sense sharp and for the case X = L-1, the conditions are even necessary and sufficient. Moreover, a new Holder type inequality is proved.

  • 131.
    Jain, Pankaj
    et al.
    Department of Mathematics, University of Delhi.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Carleman-Knopp type inequalities via Hardy inequalities2001In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 4, no 3, p. 343-355Article in journal (Refereed)
    Abstract [en]

    Some new Carleman-Knopp type inequalities are proved as "end point" inequalities of modern forms of Hardy's inequalities. Both finite and infinite intervals are considered and both the cases p q and q < p are investigated. The obtained results are compared with similar results in the literature and the sharpness of the constants is discussed for the power weight case. Moreover, some reversed Carleman-Knopp inequalities are derived and applied.

  • 132. Jain, Pankaj
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    From Hardy to Carleman and general mean-type inequalities2000In: Function spaces and applications: papers presented at an international conference held at the University of Delhi, on December 15-19, 1997. / [ed] David Eric Edmunds, University of Dehli , 2000, p. 117-130Conference paper (Refereed)
  • 133.
    Jain, Pankaj
    et al.
    Department of Mathematics, Deshbandhu College, University of Delhi.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Multidimensional Cochran and Lee type inequalities with weights2002In: Proceedings of A. Razmadze Mathematical Institute, ISSN 1512-0007, Vol. 129, p. 17-27Article in journal (Refereed)
  • 134.
    Jain, Pankaj
    et al.
    Department of Mathematics, University of Delhi.
    Singh, Arun Pal
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On geometric mean inequalities with exponential weights2004In: Soochow Journal of Mathematics, ISSN 0250-3255, Vol. 30, no 4, p. 391-400Article in journal (Refereed)
    Abstract [en]

    For $00$ such that $$ \left(\int_0^{\infty} (G_hf(x))^qw(x)dx\right)^{\frac{1}{q}}\leq C\left(\int_0^{\infty }f^p(x) v(x)dx\right)^{\frac{1}{p}} $$ where $$ G_hf(x)=\exp \left(\frac{1}{H(x)}\int_0^x h(t)\ln f(t) dt\right), $$ $f$ is a positive function, $v$ is a weight function, $w$ is non-negative measurable almost everywhere and $$ H(x)=\int_0^xh(s)ds. $$ The operator $G_hf$ is a generalization of the geometric mean operator $$ G_f(x)=\exp \left(\frac{1}{x}\int_0^x \ln f(t) dt\right). $$ The same inequalities are obtained for $$ G'_hf(x)=\exp \left(\frac{k}{e^{kx}}\int_0^x e^{kt}\ln f(t) dt\right) $$ (this operator is not a generalized geometric mean operator), and the results are compared. The proofs follow by the reduction lemma stated in [P. Jain, L. E. Persson and A. Wedestig, Math. Inequal. Appl. 4 (2001), no. 3, 343--355; MR1841067 (2002f:26019)], and in the case of $G'_kf$, by Minkowski's integral inequality and Jensen's inequality.

  • 135. Johansson, Hans
    et al.
    Maligranda, Lech
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Inequalities for moduli of continuity and rearrangements1991In: Conference on Approximation Theory, in Kecskemét, August 6 to 11, 1990 / [ed] Károly Tandory; József Szabados, Elsevier, 1991, p. 412-423Conference paper (Refereed)
    Abstract [en]

    In this paper we consider measurable functions f from a symmetric space X on [0,1]. We prove some inequalities relating the behavior of the nonincreasing rearrangement f* and the (generalized) modulus of continuity ωX (t,f). In particular, we generalize, complement and unify some previous result by Brudnyi, Garsia and Rodemich, Milman, Osvald, Storozhenko, and Wik. We note that these inequalities have direct applications, e.g. in the theory of imbedding of symmetric spaces and Besov (Lipschitz) spaces, Fourier analysis and the theory of stochastic processes. This paper is organized in the following way: In Section 1 we give some basic definitions and other preliminaries. In Section 2 we present a generalization of the Storozhenko inequality to the case of symmetric spaces thereby sharpening a previous result of Milman. We also include a generalization of the Garsia-Rodemich inequality to these spaces. In Section 3 we present and prove the Brudnyi-Osvald-Wik inequality for the case of symmetric spaces.

  • 136.
    Johansson, Maria
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Multidimensional inequalities of Hardy and (limit) Pólya-Knopp types2012In: Analysis for science, engineering and beyond: the tribute workshop in honour of Gunnar Sparr held in Lund, May 8-9, 2008, Heidelberg: Encyclopedia of Global Archaeology/Springer Verlag, 2012, p. 267-304Chapter in book (Refereed)
  • 137.
    Johansson, Maria
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Scales of equivalent integral conditions related to Hardy type inequalities with applications2007In: Eurasian Mathematical Journal, ISSN 2077-9879, no 3, p. 22-31Article in journal (Refereed)
  • 138.
    Johansson, Maria
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    A new approach to the Sawyer and Sinnamon characterizations of Hardy's inequality for decreasing functions2008In: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176, Vol. 15, no 2, p. 295-306Article in journal (Refereed)
    Abstract [en]

    Some Hardy type inequalities for decreasing functions are characterized by one condition (Sinnamon), while others are described by two independent conditions (Sawyer). In this paper we make a new approach to deriving such results and prove a theorem, which covers both the Sinnamon result and the Sawyer result for the case where one weight is increasing. In all cases we point out that the characterizing condition is not unique and can even be chosen among some (infinite) scales of conditions.

  • 139. Johansson, Maria
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Carleman's inequality: history, proofs and some new generalizations2003In: Journal of Inequalities in Pure and Applied Mathematics, ISSN 1443-5756, E-ISSN 1443-5756, Vol. 4, no 3, article id 53Article in journal (Refereed)
    Abstract [en]

    Carleman's inequality reads where , are positive numbers. In this paper we present some simple proofs of and several remarks (e.g. historical) about the inequality and its corresponding continuous version. Moreover, we discuss and comment on some very new results. We also include some new proofs and results e.g. a weight characterization of a general weighted Carleman type inequality for the case 0 p q We also include some facts about T. Carleman and his work.

  • 140. Johansson, Maria
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Carlemans olikhet: historik, skärpningar och generaliseringar2003In: Normat, ISSN 0801-3500, Vol. 51, no 3, p. 89-108Article in journal (Refereed)
  • 141.
    Kaiblinger, N.
    et al.
    Universität Wien.
    Maligranda, Lech
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Norms in weighted 2L-spaces and Hardy operators2000In: Function spaces: the fifth conference : proceedings of the conference at Poznan, Poland / [ed] Henryk Hudzik; Leszek Skrzypczak, Marcel Dekker Incorporated , 2000, p. 205-216Conference paper (Refereed)
  • 142.
    Kaijser, Sten
    et al.
    Department of Mathematics, Uppsala University.
    Nikolova, Ludmila
    Department of Mathematics, Kliment Ohridski University of Sofia.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Hardy-type inequalities via convexity2005In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 8, no 3, p. 403-417Article in journal (Refereed)
    Abstract [en]

    A recently discovered Hardy-Pólya type inequality described by a convex function is considered and further developed both in weighted and unweighted cases. Also some corresponding multidimensional and reversed inequalities are pointed out. In particular, some new multidimensional Hardy and Pólya-Knopp type inequalities and some new integral inequalities with general integral operators (without additional restrictions on the kernel) are derived

  • 143.
    Kaijser, Sten
    et al.
    Department of Mathematics, Uppsala University.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Öberg, Anders
    Department of Mathematics and Statistics, University College of Gävle.
    On Carleman's and Knopp's inequalities2002In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 117, no 1, p. 140-151Article in journal (Refereed)
    Abstract [en]

    A sharpened version of Carleman's inequality is proved. This result unifies and generalizes some recent results of this type. Also the “ordinary” sum that serves as the upper bound is replaced by the corresponding Cesaro sum. Moreover, a Carleman-type inequality with a more general measure is proved and this result may also be seen as a generalization of a continuous variant of Carleman's inequality, which is usually referred to as Knopp's inequality. A new elementary proof of (Carleman–)Knopp's inequality and a new inequality of Hardy–Knopp type is pointed out

  • 144.
    Kalybay, Aigerim A.
    et al.
    Eurasian National University, Astana.
    Oinarov, Ryskul
    Eurasian National University, Astana.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Spectral properties of a class of singular differential operators2006Report (Other academic)
  • 145.
    Kalybay, Aigerim A.
    et al.
    Institute of Mathematics, Kazakhstan Ministry of Education and Sciences.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Three weights higher order Hardy type inequalities2006In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 4, no 2, p. 163-191Article in journal (Refereed)
  • 146.
    Kalybay, Aigerim A.
    et al.
    Institute of Mathematics, Kazakhstan Ministry of Education and Sciences.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Three weights higher order Hardy type inequalities2005Report (Other academic)
  • 147.
    Kalybay, Aigerim A.
    et al.
    Eurasian National University, Astana, Institute of Mathematics, Kazakhstan Ministry of Education and Sciences, KIMEP University, Abai Ave. 4, Almaty.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Temirkhanova, Ainur
    Faculty of Mathematics and Information Technologies, Eurasian National University, Munaitpasov st., 5, Astana.
    A New discrete Hardy-type inequality with kernels and monotone functions2015In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, article id 321Article in journal (Refereed)
    Abstract [en]

    new discrete Hardy-type inequality with kernels and monotone functions is proved for the case \(1< q< p<\infty\). This result is discussed in a general framework and some applications related to Hölder’s summation method are pointed out.

  • 148.
    Kalybay, Aigerim
    et al.
    Eurasian National University, Astana.
    Oinarov, Ryskul
    Eurasian National University, Astana.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Spectral properties of a class of singular differential operators2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 3, p. 355-376Article in journal (Refereed)
  • 149.
    Kaminska, Anna
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Memphis.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Convexity, concavity, type and cotype of Lorentz spaces1996In: Séminaire d'initiation à l'analyse, Vol. 35, no 20Article in journal (Refereed)
  • 150. Kaminska, Anna
    et al.
    Maligranda, Lech
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Convexity, concavity, type and cotype of Lorentz spaces2009Conference paper (Refereed)
1234567 101 - 150 of 364
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