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  • 1.
    Ericsson, Stefan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    The E and K functionals for the pair (X(A),l∞ (B))1997In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 48, no 4, p. 479-486Article in journal (Refereed)
  • 2.
    Kato, Mikio
    et al.
    Kyushu Institute of Technology. Department of Mathematics.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Takahashi, Yasuji
    Okayama Prefactural University. Department of Systems Engineering.
    Clarkson type inequalities and their relations to the concepts of type and cotype2000In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 51, no 3, p. 327-346Article in journal (Refereed)
    Abstract [en]

    We prove some multi-dimensional Clarkson type inequalities for Banach spaces. The exact relations between such inequalities and the concepts of type and cotype are shown, which gives a conclusion in an extended setting to M. Milman's observation on Clarkson's inequalities and type. A similar investigation concerning the close connection between random Clarkson inequality and the corresponding concepts of type and cotype is also included. The obtained results complement, unify and generalize several classical and some recent results of this type.

  • 3.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Weighted inequalities for monotone functions1997In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 48, no 4, p. 687-700Article in journal (Refereed)
    Abstract [en]

    We give characterizations of weights for which reverse inequalities of theH¨oldertype for monotone functions are satisfied. Our inequalities with general weightsand with sharp constants complement the results of [2], [6], [7] and [14], [15]for the values of parameters 0 < p ≤ q < ∞.

  • 4.
    Maligranda, Lech
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Inequalities and interpolation: third International Conference "Function Spaces" (Poznan, 1992)1993In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 44, no 1, p. 181-199Article in journal (Refereed)
    Abstract [en]

    It is well known that real as well as complex interpolation is closely related to corresponding inequalities for functions, sequences, operators, s-numbers, etc. The present paper is a survey about this interrelation. The list of references contains 66 items. The authors prove classical and more recent inequalities via interpolation techniques in a rather systematic way.

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