New examples of K-monotone weighted Banach couples

Sergey V. Astashkin, Lech Maligranda, Konstantin E. Tikhomirov

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Some new examples of K-monotone couples of the type (X;X(ω)), where X is a symmetric space on [0; 1] and ω is a weight on [0; 1], are presented. Based on the property of ω-decomposability of a symmetric space we show that, if a weight ω changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X;X(ω)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t1/p for some p ⋯ [1;∞], then X = Lp. At the same time a Banach couple (X;X(ω)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space, we find conditions which guarantee that (X;X(ω)) is K-monotone.

Original languageEnglish (US)
Pages (from-to)55-88
Number of pages34
JournalStudia Mathematica
Volume218
Issue number1
DOIs
StatePublished - Nov 15 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • K-functional
  • K-method of interpolation
  • K-monotone couples
  • Lorentz spaces
  • Marcinkiewicz spaces
  • Omega;-decomposable Banach lattices
  • Orlicz spaces
  • Regularly varying functions
  • Symmetric spaces
  • Ultrasymmetric spaces
  • Weighted symmetric spaces

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  • Cite this

    Astashkin, S. V., Maligranda, L., & Tikhomirov, K. E. (2013). New examples of K-monotone weighted Banach couples. Studia Mathematica, 218(1), 55-88. https://doi.org/10.4064/sm218-1-4