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  • 1.
    Abdikalikova, Zamira
    et al.
    L.N. Gumilyov Eurasian National University.
    Oinarov, Ryskul
    L.N. Gumilyov Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 12011Ingår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 61, nr 1, s. 7-26Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a new Sobolev type function space called the space with multiweighted derivatives W-p(n),(alpha) over bar, where (alpha) over bar = (alpha(0), alpha(1), ......, alpha(n)), alpha(i) is an element of R, i = 0, 1,......,n, and parallel to f parallel to W-p(n),((alpha) over bar) = parallel to D((alpha) over bar)(n)f parallel to(p) + Sigma(n-1) (i=0) vertical bar D((alpha) over bar)(i)f(1)vertical bar, D((alpha) over bar)(0)f(t) = t(alpha 0) f(t), d((alpha) over bar)(i)f(t) = t(alpha i) d/dt D-(alpha) over bar(i-1) f(t), i = 1, 2, ....., n. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W-p,(alpha) over bar(n) -> W-q,(beta) over bar,(m) when 1 <= q < p < infinity, 0 <= m < n

  • 2.
    Abdikalikova, Zamira
    et al.
    L.N. Gumilyov Eurasian National University.
    Oinarov, Ryskul
    L.N. Gumilyov Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q2009Rapport (Övrigt vetenskapligt)
  • 3.
    Abramovic, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Tromsø ; The Arctic University of Norway, Narvik.
    Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017Ingår i: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, nr 5-6, s. 599-609Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Abstract—Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

  • 4.
    Abramovich, S.
    et al.
    Department of Mathematics, University of Haifa, Haifa, Israel.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UIT The Arctic University of Norway, Narvik, Norway.
    Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities2018Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 3, s. 759-772Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .

  • 5.
    Abramovich, Shosana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 32014Ingår i: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 / [ed] Manuel Cepedello Boiso; Håkan Hedenmalm; Marinus A. Kaashoek; Alfonso Montes Rodríguez; Sergei Treil, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2014, s. 1-10Konferensbidrag (Refereegranskat)
    Abstract [en]

    For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest

  • 6.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Krulić, Kristina
    Faculty of Textile Technology, University of Zagreb.
    Pečarić, Josip
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new refined Hardy type inequalities with general kernels and measures2010Ingår i: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 79, nr 1-2, s. 157-172Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator Ak defined by, where k: Ω1 × Ω2 is a general nonnegative kernel, (Ω1, μ1) and (Ω2, μ2) are measure spaces and,. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.

  • 7.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Inequalities for averages of quasiconvex and superquadratic functions2016Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, s. 535-550Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.

  • 8.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new estimates of the ‘Jensen gap’2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, artikel-id 39Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.

  • 9.
    Abramovich, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new scales of refined Hardy type inequalities via functions related to superquadracity2013Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, nr 3, s. 679-695Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved

  • 10.
    Abramovich, Shoshana
    et al.
    University of Haifa, Department of Mathematics.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Pecaric, Josip
    University of Zagreb.
    Varosanec, Sanja
    University of Zagreb.
    General inequalities via isotonic subadditive functionals2007Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, nr 1, s. 15-28Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

  • 11.
    Abramovich, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On some new developments of Hardy-type inequalities2012Ingår i: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2012, s. 739-746Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.

  • 12.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities2015Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, nr 2, s. 615-627Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.

  • 13.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new scales of refined Jensen and Hardy type inequalities2014Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, nr 3, s. 1105-1114Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.

  • 14.
    Abylayeva, Akbota M.
    et al.
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
    Oinarov, Ryskul
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Boundedness and compactness of a class of Hardy type operators2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikel-id 324Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.

  • 15.
    Abylayeva, Akbota M.
    et al.
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, Tromso, Norway. RUDN University, Moscow, Russia.
    Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 1, s. 201-215, artikel-id 21-16Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We establish criteria for both boundedness and compactness for some classes of integraloperators with logarithmic singularities in weighted Lebesgue spaces for cases 1 < p 6 q <¥ and 1 < q < p < ¥. As corollaries some corresponding new Hardy inequalities are pointedout.1

  • 16.
    Abylayeva, A.M.
    et al.
    L. N.Gumilev Eurasian National University, Khazakstan.
    Baiarystanov, A.O.
    L. N.Gumilev Eurasian National University, Khazakstan.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, nr 3, s. 683-694Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Abstract. Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

  • 17. Adeleke, E.
    et al.
    Cizmesija, A.
    Oguntuase, James
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Pokaz, D.
    On a new class of Hardy-type inequalities2012Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, nr 259Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy's, Hardy-Hilbert's, Hardy-Littlewood-P\'{o}lya's and P\'{o}lya-Knopp's inequalities as well as of Godunova's and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.

  • 18.
    Akhmetkaliyeva, Raya D.
    et al.
    Department of Pure Mathematics, Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Mathematics, Narvik University College.
    Ospanov, K.N.
    Department of Pure Mathematics, Eurasian National University.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new results concerning a class of third-order differential equations2015Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, nr 2, s. 419-434Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the following third-order differential equation with unbounded coefficients:Some new existence and uniqueness results are proved, and precise estimates of the norms of the solutions are given. The obtained results may be regarded as a unification and extension of all other results of this type

  • 19.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Dasht, Johan
    Glavatskih, Sergei
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Marklund, Pär
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sahlin, Fredrik
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of the Reynolds equation2005Rapport (Övrigt vetenskapligt)
  • 20.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Essel, Emmanuel Kwame
    Persson, Lars-Erik
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of the unstationary incompressible Reynolds equation2007Ingår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, nr 9, s. 1344-1350Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.

  • 21.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Glavatskih, Sergei
    Larsson, Roland
    Marklund, Pär
    Sahlin, Fredrik
    Dasht, Johan
    Persson, Lars-Erik
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of Reynolds equation2005Rapport (Övrigt vetenskapligt)
  • 22.
    Andersson, Lennart
    et al.
    Luleå tekniska universitet.
    Grennberg, Anders
    Hedberg, Torbjörn
    Luleå tekniska universitet.
    Näslund, Reinhold
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    von Sydow, Björn
    Luleå tekniska universitet.
    Linjär algebra med geometri1990 (uppl. 2)Bok (Övrig (populärvetenskap, debatt, mm))
  • 23.
    Andersson, Lennart
    et al.
    Luleå tekniska universitet.
    Grennberg, Anders
    Hedberg, Torbjörn
    Luleå tekniska universitet.
    Näslund, Reinhold
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    von Sydow, Björn
    Luleå tekniska universitet.
    Linjär algebra med geometri1986Bok (Övrig (populärvetenskap, debatt, mm))
  • 24.
    Andersson, Lennart
    et al.
    Luleå tekniska universitet.
    Grennberg, Anders
    Hedberg, Torbjörn
    Luleå tekniska universitet.
    Näslund, Reinhold
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    von Sydow, Björn
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Linjär algebra med geometri1999Bok (Övrig (populärvetenskap, debatt, mm))
  • 25.
    Arendarenko, L. S.
    et al.
    Department of Fundamental and Applied Mathematics, Eurasian National University, Munaitpasov str. 4, Astana.
    Oinarov, R.
    Department of Fundamental and Applied Mathematics, Eurasian National University, Munaitpasov str. 4, Astana.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some New Hardy-type Integral Inequalities on Cones of Monotone Functions2013Ingår i: Advances in Harmonic Analysis and Operator Theory: The Stefan Samko Anniversary Volume, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2013, s. 77-89Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Some new Hardy-type inequalities with Hardy-Volterra integral operators on the cones of monotone functions are obtained. The case 1 < p ≤ q < ∞ is considered and the involved kernels satisfy conditions which are less restrictive than the classical Oinarov condition.

  • 26.
    Arendarenko, Larissa
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    Oinarov, Ryskul
    L.N. Gumilyov Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On the boundedness of some classes of integral operators in Lebesgue spaces2011Rapport (Övrigt vetenskapligt)
  • 27.
    Arendarenko, Larissa
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    Oinarov, Ryskul
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On the boundedness of some classes of integral operators in weighted Lebesgue spaces2012Ingår i: Eurasian Mathematical Journal, ISSN 2077-9879, Vol. 3, nr 1, s. 5-17Artikel i tidskrift (Refereegranskat)
  • 28.
    Arendarenko, Larissa
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    Oinarov, Ryskul
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new inequalities on cones of monotone functions2011Rapport (Övrigt vetenskapligt)
  • 29. Asekritova, Irina
    et al.
    Kruglyak, Natan
    Maligranda, Lech
    Nikolova, Ludmila
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lions-Peetre reiteration formulas for triples and their applications2001Ingår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 145, nr 3, s. 219-254Artikel i tidskrift (Refereegranskat)
    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.

  • 30.
    Asekritova, Irina U.
    et al.
    Yaroslavl Pedagogical Institute.
    Kruglyak, Natan
    Maligranda, Lech
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Distribution and rearrangement estimates of the maximal function and interpolation1997Ingår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 124, nr 2, s. 107-132Artikel i tidskrift (Refereegranskat)
  • 31.
    Baramidze, Lasha
    et al.
    Department of Mathematics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sharp Hp- Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikel-id 242Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove and discuss some new Hp-Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out

  • 32.
    Barza, S.
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Marcoci, A.N.
    Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Best constants between equivalent norms in Lorentz sequence spaces2012Ingår i: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 2012Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.

  • 33.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Burenkov, Victor
    School of Mathematics, University College Cardiff.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sharp multidimensional multiplicative inequalities for weighted Lp spaces with homogeneous weights1998Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, nr 1, s. 53-67Artikel i tidskrift (Refereegranskat)
  • 34.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Heinig, Hans P.
    Department of Mathematics and Statistics, McMaster University, Hamilton.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Duality theorem over the cone of monotone functions and sequences in higher dimensions2002Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 7, nr 1, s. 79-108Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let f be a non-negative function defined on ℝ+n which is monotone in each variable separately. If 1 < p < ∞, g ≥ 0 and v a product weight function, then equivalent expressions for sup ∫ℝ(+)(n) fg/(ℝ+nfpv)1/p are given, where the supremum is taken over all such functions f. Variants of such duality results involving sequences are also given. Applications involving weight characterizations for which operators defined on such functions (sequences) are bounded in weighted Lebesgue (sequence) spaces are also pointed out.

  • 35.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Johansson, Maria
    Luleå tekniska universitet, Institutionen för konst, kommunikation och lärande, Pedagogik språk och Ämnesdidaktik.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    A Sawyer duality principle for radially monotone functions in Rn2005Ingår i: Journal of Inequalities in Pure and Applied Mathematics, ISSN 1443-5756, E-ISSN 1443-5756, Vol. 6, nr 2, artikel-id 44Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let f be a non-negative function on ℝn, which is radially monotone (0 < f↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup ∫ℝ fg/f↓r(∫ℝn fp v)1/p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given. © 2005 Victoria University

  • 36.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Kaminska, Anna
    Department of Mathematical Sciences, University of Memphis.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sori, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona.
    Mixed norm and multidimensional Lorentz spaces2005Rapport (Övrigt vetenskapligt)
  • 37.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Kaminska, Anna
    Department of Mathematical Sciences, University of Memphis.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Soria, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona.
    Mixed norm and multidimensional Lorentz spaces2006Ingår i: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 10, nr 3, s. 539-554Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces.

  • 38.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Marcoci, Anca
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Optimal estimates between equivalent norms in Lorentz sequence spaces2009Rapport (Övrigt vetenskapligt)
  • 39.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Marcoci, Anca-Nicoleta
    Technical University of Civil Engineering Bucharest, Department of Mathematics & Computer Science.
    Marcoci, Liviu-Gabriel
    Technical University of Civil Engineering Bucharest, Department of Mathematics & Computer Science.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Optimal estimates in Lorentz spaces of swquences with an increasing weight2013Ingår i: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 14, nr 1, s. 20-27Artikel i tidskrift (Refereegranskat)
  • 40.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Carlson type inequalities1998Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2, nr 2, s. 121-135Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A scale of Carlson type inequalities are proved and the best constants are found. Some multidimensional versions of these inequalities are also proved and it is pointed out that also a well-known inequality by Beurling-Kjellberg is included as an endpoint case.

  • 41.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Reversed Hölder type inequalities for monotone functions of several variables1997Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 186, nr 67-80, s. 67-80Artikel i tidskrift (Refereegranskat)
  • 42.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Weighted multidimensional inequalities for monotone functions1999Ingår i: Mathematica Bohemica, ISSN 0862-7959, Vol. 124, nr 2-3, s. 329-335Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We discuss the characterization of the inequality $$ \biggl(\int_{{\Bbb R}^N_+} f^q u\biggr)^{1/q} \leq C \biggl(\int_{{\Bbb R}^N_+} f^p v \biggr)^{1/p},\quad0

  • 43.
    Barza, Sorina
    et al.
    Karlstads Universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Popa, Emil C.
    Lucian Blaga University of Sibiu.
    Some multiplicative inequalities for inner products and of the Carlson type2008Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242XArtikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.

  • 44.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Popa, Nicolae
    Institute of Mathematics of Romanian Academy.
    A matriceal analogue of Fejer's theory2003Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 260, nr 1, s. 14-20Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    J. Arazy [1] pointed out that there is a similarity between functions defined on the torus and infinite matrices. In this paper we discuss and develop in the framework of matrices Fejer's theory for Fourier series.

  • 45. Barza, Sorina
    et al.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Rakotondratsiba, Yves
    On weighted multidimensional integral inequalities for mixed monotone functions2000Ingår i: Societe des Sciences Mathematiques de Roumanie. Bulletin Mathematique, ISSN 1220-3874, Vol. 43(91), nr 1, s. 39-45Artikel i tidskrift (Refereegranskat)
  • 46.
    Barza, Sorina
    et al.
    Karlstads Universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new sharp limit Hardy-type inequalities via convexity2014Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2014, artikel-id 6Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Some new limit cases of Hardy-type inequalities are proved, discussed and compared. In particular, some new refinements of Bennett's inequalities are proved. Each of these refined inequalities contain two constants, and both constants are in fact sharp. The technique in the proofs is new and based on some convexity arguments of independent interest.

  • 47.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Soria, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona.
    Multidimensional rearrangement and Lorentz spaces2004Ingår i: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 104, nr 3, s. 203-224Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.

  • 48.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Soria, Javier
    Departamento de Matemàtica, Aplicada i Anàlisi, Universitat de Barcelona.
    Sharp weighted multidimensional integral inequalities of Chebyshev type1999Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 236, nr 2, s. 243-253Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove a general Chebyshev inequality for monotone functions in higher dimensions. This result generalizes the classical one-dimensional inequality and recovers some extensions already known for product weights. In all cases we find the best constant in the inequality. We also consider the case of more general operators.

  • 49. Barza, Sorina
    et al.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Stepanov, Vladimir D.
    Computing Centre, Russian Academy of Sciences, Far-Eastern Branch, Khabarovsk.
    On weighted multidimensional embeddings for monotone functions2001Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 88, nr 2, s. 303-319Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We characterize the inequality (∫RN+ fqu)1/q ≤ C(∫RN+fpv)1/p, 0 < q, p < ∞, for monotone functions f ≥ 0 and nonnegative weights u and v. The case q < p is new and the case 0 < p ≤ q < ∞ is extended to a modular inequality with N-functions. A remarkable fact concerning the calculation of C is pointed out

  • 50.
    Baǐarystanov, Askar O.
    et al.
    Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. The Artic University of Norway.
    Shaimardan, Serikbol
    Eurasian National University.
    Temirkhanova, Ainur
    Eurasian National University.
    Some new hardy-type inequalities in q-analysis2016Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 10, nr 3, s. 761-781Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q-analogs of (r, p)-weighted Hardy-type inequalities for all possible positive values of the parameters r and p. We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction

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