Lars-Erik Persson

Luleå University of Technology, Luleå, Norrbotten, Sweden

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Publications (72)19.69 Total impact

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    Lech Maligranda, Ryskul Oinarov, Lars-Erik Persson
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    ABSTRACT: Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.
    03/2014;
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    ABSTRACT: In this paper we characterize the validity of the Hardy-type inequality \begin{equation*} \left\|\left\|\int_s^{\infty}h(z)dz\right\|_{p,u,(0,t)}\right\|_{q,w,\infty}\leq c \,\|h\|_{1,v,\infty} \end{equation*} where $0<p< \infty$, $0<q\leq +\infty$, $u$, $w$ and $v$ are weight functions on $(0,\infty)$. 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.
    Journal of Inequalities and Applications 11/2013; 2013(515). · 0.82 Impact Factor
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    ABSTRACT: We prove that the weighted Stieltjes inequality ∞ 0 ∞ 0 h(t)dt (x + t) λ q u(x)dx 1/q ≤ C ∞ 0 h p (x)v(x)dx 1/ p can be characterized by four different scales of conditions also for the case 0 < q < p < ∞, 1 < p. In particular, a new proof of a result of G. Sinnamon [10] is given, which also covers the case 0 < q < 1. 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. C 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    Mathematische Nachrichten 11/2013; · 0.58 Impact Factor
  • Dag Lukkassen, Lars-Erik Persson, Stefan Samko, Peter Wall
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    ABSTRACT: We study the boundedness of weighted multidimensional Hardy-type operators and of variable order , with radial weight , from a variable exponent locally generalized Morrey space to another . The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined by , , and , the belongness of which to the resulting space is sufficient for such a boundedness. Under additional assumptions on , this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functions and .
    Journal of function spaces and applications 10/2013; 2013. · 0.58 Impact Factor
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    Amiran Gogatishvili, Alois Kufner, Lars-Erik Persson
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    ABSTRACT: 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.
    Mathematische Nachrichten 05/2013; 286(7):659 – 668. · 0.58 Impact Factor
  • Shoshana Abramovich, Lars-Erik Persson, Natasha Samko
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    ABSTRACT: 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.
    11/2012;
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    ABSTRACT: In this paper we study boundedness of commutators of the multi-dimensional Hardy type operators with BMO coefficients, in weighted global and/or local generalized Morrey spaces LΠp,J(Rn,w) and vanishing local Morrey spaces VLlocp,J(Rn,w) defined by an almost increasing function J(r) and radial type weight w(|x|). This study is made in the perspective of posterior applications of the weighted results to some problems in the theory of PDE. We obtain sufficient conditions, in terms of some integral inequalities imposed on J and w, and also in terms of the Matuszewska-Orlicz indices of J and w, for such a boundedness.
    11/2012;
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    Alois Kufner, Komil Kuliev, Lars-Erik Persson
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    ABSTRACT: We investigate the k-th order Hardy inequality (1.1) for functions satisfying rather general boundary conditions (1.2), show which of these conditions are admissible and derive sufficient, and necessary and sufficient, conditions (for 0 < q < ∞, p > 1) on u, v for (1.1) to hold.
    Journal of Inequalities and Applications 01/2012; 2012(1). · 0.82 Impact Factor
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    Ludmila Nikolova, Lars-Erik Persson, Sanja Varošanec
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    ABSTRACT: Let be a concave function with . There is a corresponding map for which the inverse Minkowski inequality holds. Several properties of that map are obtained. Also, we consider the Beckenbach-Dresher type inequality connected with ψ-direct sums of Banach spaces and of ordered spaces. In the last section we investigate the properties of functions ψ ω,q and ∥.∥ω,q , (0 < ω < 1, q < 1) related to the Lorentz sequence space. Other posibilities for parameters ω and q are considered, the inverse Holder inequalities and more variants of the Beckenbach-Dresher inequalities are obtained. 2000 MSC: Primary 26D15; Secondary 46B99.
    Journal of Inequalities and Applications 01/2012; 2012(1). · 0.82 Impact Factor
  • Dag Lukkassen, Lars-Erik Persson, Stefan Samko
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    ABSTRACT: We study the weighted p → q -boundedness of the multidimensional weighted Hardy-type operators H w α and ℋ w α with radial type weight w = w ( | x | ) , in the generalized complementary Morrey spaces ℒ ∁ { 0 } p , ψ ( ℝ n ) defined by an almost increasing function ψ = ψ ( r ) . We prove a theorem which provides conditions, in terms of some integral inequalities imposed on ψ and w , for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the function ψ and the weight w are power functions. We also prove that the spaces ℒ ∁ { 0 } p , ψ ( Ω ) over bounded domains Ω are embedded between weighted Lebesgue space L p with the weight ψ and such a space with the weight ψ , perturbed by a logarithmic factor. Both the embeddings are sharp.
    Journal of function spaces and applications 01/2012; 2012. · 0.58 Impact Factor
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    Yulia Koroleva, Lars-Erik Persson, Peter Wall
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    ABSTRACT: This article is devoted to the Friedrichs inequality, where the domain is periodically perforated along the boundary. It is assumed that the functions satisfy homogeneous Neumann boundary conditions on the outer boundary and that they vanish on the perforation. In particular, it is proved that the best constant in the inequality converges to the best constant in a Friedrichs-type inequality as the size of the perforation goes to zero much faster than the period of perforation. The limit Friedrichs-type inequality is valid for functions in the Sobolev space H 1. AMS 2010 Subject Classification: 39A10; 39A11; 39A70; 39B62; 41A44; 45A05.
    Journal of Inequalities and Applications 01/2011; 2011(1). · 0.82 Impact Factor
  • Lars-Erik Persson, Natasha Samko
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    ABSTRACT: We study the weighted p→q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces Lp,φ(Rn,w) defined by an almost increasing function φ(r) and radial type weight w(|x|). We obtain sufficient conditions, in terms of some integral inequalities imposed on φ and w, for such a p→q-boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p→q-boundedness of the Riesz potential operator.
    Journal of Function Spaces and Applications 01/2011; 377(2):792-806. · 0.50 Impact Factor
  • Lars-Erik Persson, Natasha Samko
    09/2010;
  • Lars-Erik Persson, Natasha Samko
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    ABSTRACT: We consider singular integral equations with discontinuous coefficients in generalized weighted Morrey spaces. We prove a result on Fredholmness of such equations. Moreover, we give explicit formulas showing direct dependence of the number of solutions on the parameters defining the space. Finally we apply our result to derive concrete solutions, in this space, of Sönghen equation which is of great interest in aerodynamics.
    09/2010;
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    ABSTRACT: We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator A k defined by $ A_kf(x):=\frac{1}{K(x)} \int\limits_{\Omega_2} k(x,y)f(y)d\mu_2(y), $ A_kf(x):=\frac{1}{K(x)} \int\limits_{\Omega_2} k(x,y)f(y)d\mu_2(y), where k: W1 W2 ® \mathbbR{k: \Omega_1 \times \Omega_2 \to \mathbb{R}} is a general nonnegative kernel, (Ω1, μ 1) and (Ω2, μ 2) are measure spaces and K(x):=òW2 k(x,y)dm2(y), x Î W1. K(x):=\int\limits_{\Omega_2} k(x,y)d\mu_2(y), \, x \in \Omega_1. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained. Mathematics Subject Classification (2000)Primary 26D10-Secondary 26D15 KeywordsInequalities-Hardy’s inequality-Hardy–Hilbert’s inequality-kernels-measures-Hardy type operators-superquadratic function-subquadratic function-integral identities
    Aequationes Mathematicae 01/2010; 79(1):157-172. · 0.42 Impact Factor
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    ABSTRACT: We consider a quasilinear parabolic problem with time dependent coefficients oscillating rapidly in the space variable. The existence and uniqueness results are proved by using Rothe’s method combined with the technique of two-scale convergence. Moreover, we derive a concrete homogenization algorithm for giving a unique and computable approximation of the solution. Keywordsparabolic PDEs-Rothe’s method-two-scale convergence-homogenization of periodic structures-homogenization algorithm MSC 201035K55-74Q15
    Applications of Mathematics 01/2010; 55(4):305-327. · 0.22 Impact Factor
  • Source
    Amiran Gogatishvili, Alois Kufner, Lars-Erik Persson
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    ABSTRACT: 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.
    Proceedings of the Estonian Academy of Sciences 01/2010; 59(1):7-18. · 0.31 Impact Factor
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    Dag Lukkassen, Annette Meidell, Lars-Erik Persson
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    ABSTRACT: We consider homogenization of sequences of integral functionals with natural growth conditions. Some means are analyzed and used to discuss some fairly new bounds for the homogenized integrand corresponding to integrands which are periodic in the spatial variable. These bounds, which are obtained by variational methods, are compared with the nonlinear bounds of Wiener and Hashin–Shtrikman type. We also point out conditions that make our bounds sharp. Several applications are presented. Moreover, we also discuss bounds for some linear reiterated two-phase problems with m different micro-levels in the spatial variable. In particular, the results imply that the homogenized integrand becomes optimal as m turns to infinity. Both the scalar case (the conductivity problem) and the vector-valued case (the elasticity problem) are considered. In addition, we discuss bounds for estimating the effective behavior described by homogenizing a problem which is a generalization of the Reynold equation.
    01/2010;
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    AMIRAN GOGATISHVILI, ALOIS KUFNER, LARS-ERIK PERSSON
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    ABSTRACT: 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.
    Acta Mathematica Hungarica 01/2009; 123(4):365-377. · 0.35 Impact Factor
  • Sorina Barza, Lars-Erik Persson
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    ABSTRACT: Some weighted modular integrals inequalities with Volterra type operators are considered. The equivalence of such inequalities on the cones on non-negative respective non-increasing functions is established.
    12/2008: pages 53-59;

Publication Stats

370 Citations
19.69 Total Impact Points

Institutions

  • 1995–2013
    • Luleå University of Technology
      • • Department of Engineering Sciences and Mathematics
      • • Division of Machine Elements
      Luleå, Norrbotten, Sweden
  • 2010
    • University of West Bohemia
      Pilsen, Plzeňský, Czech Republic
  • 1997–2004
    • Lund University
      • Division of Mathematics
      Lund, Skåne, Sweden