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

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

  • 2.
    Aksoy, A.G.
    et al.
    Department of Mathematics, Claremont McKenna College.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lipschitz-Orlicz spaces and the Laplace equation1996In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, no 178, p. 81-101Article in journal (Refereed)
  • 3.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Reversed Hölder type inequalities for monotone functions of several variables1997In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 186, no 67-80, p. 67-80Article in journal (Refereed)
  • 4.
    Barza, Sorina
    et al.
    Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Popa, Nicolae
    Institute of Mathematics of Romanian Academy.
    A matriceal analogue of Fejer's theory2003In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 260, no 1, p. 14-20Article in journal (Refereed)
    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.

  • 5.
    Bergh, Jöran
    et al.
    Chalmers University of Technology, Department of Mathematics.
    Burenkov, Victor
    Department of Differential Equations and Functional Analysis, Russian Peoples' Friendship University.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On some sharp reversed Hölder and Hardy type inequalities1994In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, no 169, p. 19-29Article in journal (Refereed)
  • 6.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norway, Narvik, Norway.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces2018In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, no 11-12, p. 1655-1665Article in journal (Refereed)
    Abstract [en]

    We study one‐ and multi‐dimensional weighted Hardy operators on functions with Hölder‐type behavior. As a main result, we obtain necessary and sufficient conditions on the power weight under which both the left and right hand sided Hardy operators map, roughly speaking, functions with the Hölder behavior only at the singular point to functions differentiable for and bounded after multiplication by a power weight. As a consequence, this implies necessary and sufficient conditions for the boundedness in Hölder spaces due to the corresponding imbeddings. In the multi‐dimensional case we provide, in fact, stronger Hardy inequalities via spherical means. We also separately consider the case of functions with Hölder‐type behavior at infinity (Hölder spaces on the compactified ).

  • 7.
    Cheng, Yanji
    Luleå University of Technology.
    An eigenvalue problem for a quasilinear elliptic equation1998In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 196, p. 43-59Article in journal (Refereed)
  • 8.
    Dechevski, Ljubomir T.
    et al.
    Department of Numerical Methods and Analysis, Technical University, Sofia.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sharp generalized Carleman inequalities with minimal information about the spectrum1994In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 168, p. 61-77Article in journal (Refereed)
  • 9.
    Ericsson, Stefan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Descriptions of some K functionals for three spaces and reiteration1999In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 202, p. 29-41Article in journal (Refereed)
  • 10.
    Gasch, J.
    et al.
    Department of Mathematics, Central University of Venezuela.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On vector-valued inequalities of the Marcinkiewicz-Zygmund, Herz and Krivine type1994In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 167, p. 95-129Article in journal (Refereed)
  • 11.
    Gogatishvili, Amiran
    et al.
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Kufner, Alois
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Weighted Stieltjes inequality and applications2013In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 286, no 7, p. 659-668Article in journal (Refereed)
    Abstract [en]

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

  • 12.
    Gogatishvili, Amiran
    et al.
    Institute of Mathematics of the Academy of Sciences of the Czech Republic.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir D.
    Department of Mathematical Analysis, Russian Peoples' Friendship University.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some scales of equivalent conditions to characterize the Stieltjes inequality: the case q2014In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 287, no 2-3, p. 242-253Article in journal (Refereed)
    Abstract [en]

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

  • 13.
    Kolwicz, Pawel
    et al.
    Institute of Mathematics of Electric Faculty, Poznań University of Technology.
    Lesnik, Karol
    Institute of Mathematics of Electric Faculty, Poznań University of Technology.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Pointwise multipliers of Calderón-Lozanovskiǐ spaces2013In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 286, no 8-9, p. 876-907Article in journal (Refereed)
    Abstract [en]

    Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calderón-Lozanovskiǐ spaces are proved. We investigate assumptions on a Banach ideal space E and three Young functions φ1, φ2 and φ, generating the corresponding Calderón-Lozanovskiǐ spaces so that the space of multipliers of all measurable x such that x y ∈ Eφ for any can be identified with . Sufficient conditions generalize earlier results by Ando, O'Neil, Zabreǐko-Rutickiǐ, Maligranda-Persson and Maligranda-Nakai. There are also necessary conditions on functions for the embedding to be true, which already in the case when E = L1, that is, for Orlicz spaces give a solution of a problem raised in the book 26. Some properties of a generalized complementary operation on Young functions, defined by Ando, are investigated in order to show how to construct the function φ2 such that . There are also several examples of independent interest.

  • 14.
    Kufner, Alois
    et al.
    Mathematical Institute, Czech Academy of Sciences, Department of Mathematics, University of West Bohemia.
    Persson, Lars-Erik
    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.
    Hardy type inequalities with kernels: The current status and some new results2017In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, no 1, p. 57-65Article in journal (Refereed)
    Abstract [en]

    We consider the general Hardy type operator inline image where inline image is a positive and measurable kernel. To characterize the weights u and v so that inline image is still an open problem for any parameters p and q. However, for special cases the solution is known for some parameters p and q. In this paper the current status of this problem is described and discussed mainly for the case inline image In particular, some new scales of characterizations in classical situations are described, some new proofs and results are given and open questions are raised.

  • 15. Maligranda, Lech
    et al.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On Clarkson´s inequalities and interpolation1992In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 155, p. 187-197Article in journal (Refereed)
  • 16.
    Maligranda, Lech
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sabourova, Natalia
    On Clarkson's inequality in the real case2007In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 280, no 12, p. 1363-1375Article in journal (Refereed)
    Abstract [en]

    The best constant in a generalized complex Clarkson inequality is Cp,q () = max {21-1/p , 21/q , 21/q -1/p +1/2} which differs moderately from the best constant in the real case Cp,q () = max {21-1/p , 21/q ,Bp,q }, where . For 1 < q < 2 < p < the constant Cp,q () is equal to Bp,q and these numbers are difficult to calculate in general. As applications of the generalized Clarkson inequalities the (p, q)-Clarkson inequalities in Lebesgue spaces, in mixed norm spaces and in normed spaces are presented.

  • 17.
    Pecaric, Josip
    et al.
    Faculty of Textile Technology, University of Zagreb.
    Peric, Ivan
    Faculty of Chemical Engineering and Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    A sharp multidimensional Bergh type inequality2001In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 228, no 1, p. 155-162Article in journal (Refereed)
    Abstract [en]

    A sharp multidimensional integral inequality for functions satisfying two quasi-mono-tonicity conditions is proved. This result generalizes Bergh's inequality valid for quasi-concave functions.

  • 18.
    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.

  • 19. Simon, Ilona
    et al.
    Memić, Nacima
    Tephnadze, George
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Strong convergence of two-dimensional Vilenkin-Fourier series2016In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 289, no 4, p. 485-500Article in journal (Refereed)
    Abstract [en]

    We prove that certain means of the quadratical partial sums of the two-dimensional Vilenkin-Fourier series are uniformly bounded operators from the Hardy space inline image to the space inline image for inline image We also prove that the sequence in the denominator cannot be improved.

  • 20.
    Strömberg, Thomas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    An operation connected to a Young-type inequality1992In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 159, p. 227-243Article in journal (Refereed)
1 - 20 of 20
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