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  • 301.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sharp upper bounds for and some properties of generalized entropies1994In: Mathematica Balkanica, ISSN 0205-3217, Vol. 8, no 2-3, p. 153-164Article in journal (Refereed)
  • 302.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some elementary inequalities in connection with Xp -spaces1988In: Constructive theory of functions: proceedings of the International Conference on Constructive Theory of Functions, Varna, May 24-31, 1987 / [ed] Blagovest Sendov, Publishing House of the Bulgarian Academy of Sciences , 1988, p. 367-376Conference paper (Refereed)
  • 303.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    The homogenization method and some of its applications1993In: Mathematica Balkanica, ISSN 0205-3217, Vol. 7, no 3-4, p. 179-190Article in journal (Refereed)
  • 304.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    The way to the top of science of professor R. Oinarov: Dedicated to the 70th birthday of Professor Ryskul Oinarov2017In: Eurasian Mathematical Journal, ISSN 2077-9879, Vol. 8, no 2, p. 9-21Article in journal (Refereed)
  • 305.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    What should have happened if Hardy had invented this?2010Report (Other academic)
  • 306.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Barza, Sorina
    Equivalence of modular inequalities of Hardy type on non-negative respective non-increasing functions2009In: Inequalities and Applications / [ed] C. Bandle; A. Gilányi; L. Losonczi; Z. Páles; M. Plum, Birkhäuser Verlag, 2009, p. 53-60Conference paper (Refereed)
  • 307.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Barza, Sorina
    Luleå tekniska universitet.
    Soria, Javier
    Departamento de Matemàtica, Aplicada i Anàlisi, Universitat de Barcelona.
    Sharp weighted multidimensional integral inequalities for monotone functions2000In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 210, no 1, p. 43-58Article in journal (Refereed)
    Abstract [en]

    We prove sharp weighted inequalities for general integral operators acting on monotone functions of several variables. We extend previous results in one dimension, and also those in higher dimension for particular choices of the weights (power weights, etc.). We introduce a new kind of conditions, which take into account the more complicated structure of monotone functions in dimension n > 1, and give an example that shows how intervals are not enough to characterize the boundedness of the operators (contrary to what happens for n = 1). We also give several applications of our techniques.

  • 308.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Carro, Maria J.
    Nikolova, Ludmila Y.
    Real interpolation between families of Banach spaces and some kinds of operators2000In: Function spaces and applications: papers presented at an international conference held at the University of Delhi, on December 15-19, 1997. / [ed] David E. Edmunds, University of Dehli , 2000, p. 36-59Conference paper (Refereed)
  • 309.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Kufner, Alois
    Mathematical Institute, Czech Academy of Sciences.
    Some difference inequalities with weights and interpolation1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 3, p. 437-444Article in journal (Refereed)
    Abstract [en]

    The well-known Grisvard-Jakovlev inequality (see Theorems 1 and 1_ ) can be interpretedas a fractional order Hardy inequality or as a weighted difference inequality. Someinequalities of this type have been recently proved and discussed by the authors and H. Heinig,and this paper coincides mostly with a lecture held by the first author at the International workshopon difference and differential inequalities (July 3 - 7, 1996, Marmara Research Center,Turkey) where some historical remarks, ideas and results from the papers of the authors and H.Heinig have been presented. Additionally we present and prove some new difference inequalitieswith weights. Mostly, we omit the proofs which can be found in the papers mentioned and in thereferences there, and for simplicity, we consider functions on the interval

  • 310.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lukkassen, Dag
    Sierpinska, Anna
    Some aspects on web-courses in mathematics based on PC screen recorded video lectures2007In: Nordisk matematikkdidaktikk, ISSN 1104-2176, no 4, p. 51-70Article in journal (Refereed)
  • 311.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Maligranda, Lech
    The E-functional for some pairs of groups1991In: Results in Mathematics, ISSN 1422-6383, Vol. 20, no 1-2, p. 539-553Article in journal (Refereed)
  • 312.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Oguntuase, James
    Refinement of Hardy's inequality for "all" p.2008In: Proceedings of the 2nd international symposium on Banach and function spaces II (ISBFS 2006),: Kitakyushu, Japan, September 14-17, 2006 / [ed] Mikio Kato; Lech Maligranda, Yokohama: Yokohama Publishers, 2008, p. 129-144Conference paper (Refereed)
  • 313.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Leif
    Svanstedt, Nils
    Wyller, John
    The homogenization method: an introduction1993Book (Other (popular science, discussion, etc.))
  • 314.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Popa, Nicolae
    Simion Stoilov Institute of Mathematics, Romanian Academy, Romania & Technical University.
    Matrix Spaces and Schur Multipliers: Matriceal Harmonic Analysis2014Book (Refereed)
    Abstract [en]

    This book gives a unified approach to the theory concerning a new matrix version of classical harmonic analysis. Most results in the book have their analogues as classical or newer results in harmonic analysis. It can be used as a source for further research in many areas related to infinite matrices. In particular, it could be a perfect starting point for students looking for new directions to write their PhD thesis as well as for experienced researchers in analysis looking for new problems with great potential to be very useful both in pure and applied mathematics where classical analysis has been used, for example, in signal processing and image analysis.

  • 315.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Popova, Olga V.
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow.
    Stepanov, Vladimir D.
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow.
    Two-sided hardy-type inequalities for monotone functions2010In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 55, no 8, p. 973-989Article in journal (Refereed)
    Abstract [en]

    We consider Hardy-type operators on the cones of monotone functions with general positive σ-finite Borel measure. Some two-sided Hardy-type inequalities are proved for the parameter -∞ < p < ∞. It is pointed out that such equivalences, in particular, imply a new characterization of the discrete Hardy inequality for the (most difficult) case 0 < q < p ≤ 1

  • 316.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Popova, Olga V.
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow, Peoples' Friendship University of Russia.
    Stepanov, Vladimir D
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow, Computing Centre, Russian Academy of Sciences, Far-Eastern Branch, Khabarovsk, Computing Center, Far Eastern Scientific Center, Russian Academy of Sciences.
    Weighted Hardy-type inequalities on the cone of quasi-concave functions2014In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, no 3, p. 879-898Article in journal (Refereed)
    Abstract [en]

    The paper is devoted to the study of weighted Hardy-type inequalities on the cone of quasi-concave functions, which is equivalent to the study of the boundedness of the Hardy operator between the Lorentz Γ-spaces. For described inequalities we obtain necessary and sufficient conditions to hold for parameters q 1, p > 0 and sufficient conditions for the rest of the range of parameters.

  • 317.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Prokhorov, Dmitry
    Integral inequalities for some weighted geometric mean operators with variable limits2003Report (Other academic)
  • 318.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Prokhorov, Dmitry
    Integral inequalities for some weighted geometric mean operators with variable limits2004In: Archives of Inequalities and Applications, ISSN 1542-6149, Vol. 2, no 4, p. 475-482Article in journal (Refereed)
    Abstract [en]

    The authors introduce a new geometric mean integral operator, which is a generalization of the usual one in the sense that the limits of integration $0$ and $x$ are replaced by two functions of $x$, continuous and strictly increasing, preserving the order between them. They also consider the corresponding Hardy type operator which is obtained from the considered operator by logarithm to base $e$. The authors consider a mapping from $L_p$ to $L_q$, $q$ greater than $p$, both $p$ and $q$ positive and finite, where to $f$ from $L_p$ corresponds, in $L_q$, the product of a weighted function $v$ with image by the considered operator of $u$, where $u$ is another weighted function. They prove necessary and sufficient conditions for an inequality between the norm of $f$ and the norm of the image of $f$ through the described mapping, this latest norm being smaller than the norm of $f$. From the summary: "The key point of the proof is to first derive a similar result for the corresponding Hardy operator

  • 319.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. The Arctic University of Norway.
    Rafeiro, Humberto
    Pontificia Universidad Javeriana, Bogotá, Colombia.
    On a Taylor remainder2017In: Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, ISSN 1786-0091, E-ISSN 1786-0091, Vol. 33, no 2, p. 195-198Article in journal (Refereed)
    Abstract [en]

    In this note we derive a new Taylor remainder, which extends the well known Lagrange remainder as well as the obscure Goncalves remainder.

  • 320.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ragusa, Alessandra
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    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 some results in weighted Morrey spaces with applications to PDE2012Report (Other academic)
  • 321.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ragusa, Maria Alessandra
    University of Catania.
    Samko, Natasha
    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.
    Commutators of Hardy operators in vanishing Morrey spaces2012In: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2012, p. 859-866Conference paper (Refereed)
    Abstract [en]

    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,φ(Rn,w) and vanishing local Morrey spaces VLlocp,φ(Rn,w) defined by an almost increasing function φ(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 φ and w, and also in terms of the Matuszewska-Orlicz indices of φ and w, for such a boundedness.

  • 322.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Universidade do Algarve, FCT, Campus de Gambelas, Instituto Superior Tecnico, Research center CEAF.
    A note on the best constants in some Hardy inequalities2015In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 9, no 2, p. 437-447Article in journal (Refereed)
    Abstract [en]

    The sharp constants in Hardy type inequalities are known only in a few cases. In this paper we discuss some situations when such sharp constants are known, but also some new sharp constants are derived both in one-dimensional and multi-dimensional cases.

  • 323.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Inequalities and Convexity2014In: Operator Theory, Operator Algebras and Applications, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2014, p. 279-306Chapter in book (Refereed)
    Abstract [en]

    It is a close connection between various kinds of inequalities and the concept of convexity. The main aim of this paper is to illustrate this fact in a unified way as an introduction of this area. In particular, a number of variants of classical inequalities, but also some new ones, are derived and discussed in this general frame.

  • 324.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Universidade do Algarve, FCT, Campus de Gambelas.
    Quasi-monotone weight functions and their applications2010In: Numerical analysis and applied mathematics: International Conference on Numerical Analysis and Applied Mathematics 2010, Rhodes, Greece, 19 - 25 September 2010 / [ed] Theodore E. Simos, American Institute of Physics (AIP), 2010, p. 502-505Conference paper (Refereed)
    Abstract [en]

    Quasi-monotone functions have turned out to be very important for several applications. In this paper we present and develop a more complete theory for such functions. In particular, some new regularization results are stated and the close connection to various classes of index numbers are derived. Finally, a number of concrete applications are pointed out.

  • 325.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Session-workshop on analysis, inequalities and homogenization theory and applications2010In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1281, p. 489-Article in journal (Other academic)
    Abstract [en]

    Analysis, Inequalities and Homogenization Theory are increasingly important areas for various kinds of applications both to other fields of Mathematics and to other sciences, e.g. physics, material science, numerical analysis and geophysics.The main aim of the session is to bring together researchers with different backgrounds and interests in all aspects of these areas of mathematics and plan for future cooperation and new directions of joint research. As background the participants will present the newest developments and present “status of the art” of their research fields. Special meetings with informal discussions will be organized, where in particular various kinds of applications will be highlighted. The topics of interest include (but are not limited to): General Inequalities, Hardy type inequalities, Real and complex analysis, Functional analysis, q-analysis, Interpolation theory, Function Spaces and Homogenization Theory

  • 326.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Singular integral equations in generalized weighted Morrey spaces2010In: Numerical analysis and applied mathematics: Conference on Numerical Analysis and Applied Mathematics 2010, Rhodes, Greece, 19 - 25 September 2010 / [ed] Theodore E. Simos, American Institute of Physics (AIP), 2010, p. 498-501Conference paper (Refereed)
    Abstract [en]

    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.

  • 327.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Some remarks and new developments concerning Hardy-type inequalities2010In: Studies in the History of Modern Mathematics: Supplemento di Rendiconti del Circolo Matematico di Palermo, no 82, p. 93-122Article in journal (Refereed)
  • 328.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Weighted Hardy and potential operators in the generalized Morrey spaces2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 377, no 2, p. 792-806Article in journal (Refereed)
    Abstract [en]

    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

  • 329.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Departamento de Matemtica, Centro CEAF, Instituto Superior Tecnico.
    What should have happened if Hardy had discovered this?2012In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, no 2Article in journal (Refereed)
    Abstract [en]

    First we present and discuss an important proof of Hardy's inequality via Jensen's inequality which Hardy and his collaborators did not discover during the 10 years of research until Hardy finally proved his famous inequality in 1925. If Hardy had discovered this proof, it obviously would have changed this prehistory, and in this article the authors argue that this discovery would probably also have changed the dramatic development of Hardy type inequalities in an essential way. In particular, in this article some results concerning powerweight cases in the finite interval case are proved and discussed in this historical perspective. Moreover, a new Hardy type inequality for piecewise constant p = p(x) is proved with this technique, limiting cases are pointed out and put into this frame.

  • 330.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    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.
    Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces2016In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 22, no 2, p. 413-426Article in journal (Refereed)
    Abstract [en]

    We find conditions for the weighted boundedness of a general class of multidimensional singular integral operators in generalized Morrey spaces L p,φ (R n ,w), defined by a function φ(x,r) and radial type weight w(|x−x 0 |),x 0 ∈R n . These conditions are given in terms of inclusion into L p,φ (R n ,w), of a certain integral constructions defined by φ and w. In the case of φ=φ(r) we also provide easy to check sufficient conditions for that in terms of indices of φ and w.

  • 331.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Instituto Superior Tecnico, Research center CEAF.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Quasi-monotone weight functions and their characteristics and applications2012In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 15, no 3, p. 685-705Article in journal (Refereed)
    Abstract [en]

    A weight function w(x) on (0,l) or (l,infinity), is said to be quasi-monotone if w(x)x(-a0) <= C(0)w(y)y(-a0) either for all x <= y or for all y <= x, for some a(0) is an element of R, C-0 >= 1. In this paper we discuss, complement and unify several results concerning quasi-monotone functions. In particular, some new results concerning the close connection to index numbers and generalized Bary-Stechkin classes are proved and applied. Moreover, some new regularization results are proved and several applications are pointed out, e. g. in interpolation theory, Fourier analysis, Hardy-type inequalities, singular operators and homogenization theory.

  • 332.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, S.G.
    Universidade do Algarve, Campus de Gambelas.
    Some new Stein and Hardy type inequalities2010In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 169, no 1, p. 113-129Article in journal (Refereed)
    Abstract [en]

    We prove a generalization of the pointwise Stein inequality, considering two truncated versions. More generally than in the Stein inequality, we assume that the kernel is dominated by a radial function almost decreasing after the division by a power function with nonnegative exponent in the case of the truncation to the ball of the radius and almost increasing after the multiplication by a power function in the case of truncation to the exterior of this ball. We give some applications to a series of inequalities of Hardy type in norms of various function spaces, in particular, in the norm of variable exponent Lebesgue spaces with weights.

  • 333.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sarybekova, L.
    Eurasian National University, Astana.
    Tleukhanova, N.
    Eurasian National University, Astana.
    A Lizorkin type theorem for Fourier series multipliers in regular systems2009Report (Other academic)
  • 334.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sarybekova, Lyazzat
    Tleukhanova, N.
    Multidimensional generalization of the Lizorkin theorem on Fourier multipliers2009In: Proceedings of A. Razmadze Mathematical Institute, ISSN 1512-0007, Vol. 151, p. 83-101Article in journal (Refereed)
  • 335.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sarybekova, Lyazzat
    Gumilyov Eurasian National University.
    Tleukhanova, Nazerke
    Gumilyov Eurasian National University.
    A Lizorkin theorem on Fourier series multipliers for stron regular systems2012In: 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. 305-317Chapter in book (Refereed)
  • 336.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sarybekova, Lyazzat
    Eurasian National University, Astana.
    Tleukhanova, Nazerke
    Eurasian National University, Astana.
    Multidimensional generalization of the Lizorkin theorem on Fourier multipliers2008Report (Other academic)
  • 337.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Shaimardan, Serikbol
    L.N. Gumilyov Eurasian National University.
    Some new Hardy-type inequalities for Riemann-Liouville fractional q-integral operator2015In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, article id 296Article in journal (Refereed)
  • 338.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Narvik University College.
    Shambilova, Guldarya E.
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow.
    Stepanov, Vladimir D
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University of Russia; Steklov Mathematical Institute, Russian Academy of Sciences.
    Hardy-type inequalities on the weighted cones of quasi-concave functions2015In: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 9, no 2, p. 21-34Article in journal (Refereed)
    Abstract [en]

    The complete characterization of the Hardy-type Lp-Lq inequalities on the weighted cones of quasi-concave functions for all 0 < p, q < ∞ is given.

  • 339.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norway, Narvik, Norway.
    Shambilova, Guldarya E.
    Department of Mathematics, Financial University under the Government of the Russian Federation.
    Stepanov, Vladimir D.
    Department of Nonlinear Analysis and Optimization, Peoples’ Friendship University of Russia.
    Weighted Hardy type inequalities for supremum operators on the cones of monotone functions2016In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 1, article id 237Article in journal (Refereed)
    Abstract [en]

    The complete characterization of the weighted Lp− Lr inequalities of supremum operators on the cones of monotone functions for all 0 < p, r≤ ∞ is given.

  • 340.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sjöstrand, Sigrid
    Lund University.
    On generalized Gini means and scales of means1990In: Results in Mathematics, ISSN 1422-6383, Vol. 18, no 3-4, p. 320-332Article in journal (Refereed)
  • 341.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir D.
    Computing Center, Far Eastern Scientific Center, Russian Academy of Sciences.
    Weighted integral inequalities with a geometric mean2001In: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 377, no 4, p. 439-440Article in journal (Refereed)
  • 342.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir D.
    Computing Centre, Russian Academy of Sciences, Far-Eastern Branch, Khabarovsk.
    Weighted integral inequalities with the geometric mean operator2002In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 7, no 5, p. 727-746Article in journal (Refereed)
    Abstract [en]

    The geometric mean operator is defined by Gf(x) = exp(1/x∫0x logf(t)dt). A precise two-sided estimate of the norm ||G|| = supf≠0 ||Gf||Luq/||f||Lvq for 0 < p, q ≤ ∞ is given and some applications and extensions are pointed out

  • 343.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir D.
    Department of Mathematical Analysis, Russian Peoples' Friendship University.
    Ushakova, Elena P.
    Computing Center, Far Eastern Scientific Center, Russian Academy of Sciences.
    Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions2005Report (Other academic)
  • 344.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir D.
    Department of Mathematical Analysis, Russian Peoples' Friendship University.
    Ushakova, Elena P.
    Computing Center, Far Eastern Scientific Center, Russian Academy of Sciences.
    Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions2006In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 134, no 8, p. 2363-2372Article in journal (Refereed)
    Abstract [en]

    Some Hardy-type integral inequalities in general measure spaces, where the corresponding Hardy operator is replaced by a more general Volterra type integral operator with kernel k(x,y), are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied.

  • 345.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir
    Ushakova, Elena
    On integral operators with monotone kernels2005In: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 403, no 1, p. 11-14Article in journal (Refereed)
    Abstract [en]

    The conditions are investigated, under which for all Lebesgue measurable functions f(x) greater than or equal 0 on a semi-axis R+:=(0, infinity ) with a constant C greater than or equal 0 independent of f, satisfied is inequality: {0 integral infinity [Kf(x)]qν(x)dx}1/q [less-than or equal to] C{0 integral infinity [f(x)]pu(x)dx}1/p (1) with measurable weighted functions u(x) greater than or equal 0 and ν(x) greater than or equal 0 and integral operator Kf(x):=0 integral infinity k(x,y)f(y)dy, where measurable in R+×R+ kernel k(x,y) greater than or equal 0 is monotone in one or two variables. Such operators can be exemplified with Laplace, Hilbert transforms etc. Further, the comparison theorems for (1)-type inequalities with the similar inequalities on a cone of non-growing functions for certain-type Volterra operators are proved.

  • 346.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir
    Wall, Peter
    Some scales of equivalent weight characterizations of Hardy's inequality: the case q2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 2, p. 267-279Article in journal (Refereed)
    Abstract [en]

    We consider the weighted Hardy inequality (∫0∞ (∫0x f(t)dt)q u(x)dx)1/q ≤ C(∫0∞ f p(x)v(x)dx)1/p for the case 0 < q < p < ∝, p > 1. The weights u(x) and v(x) for which this inequality holds for all f (x) ≥ 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanov conditions. In this paper, we show that these conditions are not unique and can be supplemented by some continuous scales of conditions and we prove their equivalence. The results for the dual operator which do not follow by duality when 0 < q < 1 are also given

  • 347.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Strömberg, Thomas
    Green's method applied to the plate equation in mechanics1993In: Annales Societatis Mathematicae Polonae. Series 1: Commentationes Mathematicae - Prace Matematyczne, ISSN 0373-8299, Vol. 33, p. 119-133Article in journal (Refereed)
    Abstract [en]

    This paper demonstrates existence and uniqueness of Green functions for the general fourth-order linear elliptic operator modeling the deflection of an anisotropic elastic plate with the linear boundary conditions that model the most common edge conditions. The existence theory is presented in the context of Sobolev spaces. Included is the derivation of the boundary value problem from the principles of elasticity and of the Green function for a homogeneous rectangular plate. The paper concludes with a brief discussion of qualitative properties of the Green functions. The techniques and results are classic, and the exposition is accessible to a broad audience. This paper could serve as an admirable introduction to the boundary value problems of anisotropic plates.

  • 348.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Svanstedt, Nils
    A note on some homogenization methods1993In: Ikke angivet, Department of Mathematical Sciences, Norwegian Institute of Technology , 1993, p. 145-150Conference paper (Refereed)
  • 349.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Tephnadze, George
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    A Sharp Boundedness Result Concerning Some Maximal Operators of Vilenkin–Fejér Means2016In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 13, no 4, p. 1841-1853Article in journal (Refereed)
    Abstract [en]

    In this paper, we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fejér means in this subspace is bounded from the Hardy space Hp to the space Lp for all 0 < p ≤ 1/2. Moreover, we prove that the result is in a sense sharp

  • 350.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Tephnadze, George
    Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new (Hp,Lp) type inequalities of maximal operators of vilenkin-nörlund means with non-decreasing coefficients2015In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 9, no 4, p. 1055-1069Article in journal (Refereed)
    Abstract [en]

    In this paper we prove and discuss some new (Hp,Lp) type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients. We also apply these inequalities to prove strong convergence theorems of such Vilenkin-Nörlund means. These inequalities are the best possible in a special sense. As applications, both some well-known and new results are pointed out

45678 301 - 350 of 364
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