An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices

Alexei Karlovich, Eugene Shargorodsky

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1 Citation (Scopus)

Abstract

We show that for every p ∈ (1, ∞) there exists a weight w such that the Lorentz Gamma space Γp,w is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space Γp,w and on its associate space Γ'p,w.

Original languageEnglish
Pages (from-to)1199-1209
Number of pages11
JournalCzechoslovak Mathematical Journal
Volume71
Issue number4
DOIs
Publication statusPublished - Dec 2021

Keywords

  • 42B25
  • 46E30
  • Boyd indices
  • Lorentz Gamma space
  • reflexivity
  • Zippin indices

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