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

Eugene Shargorodsky, Alexei Karlovich

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We show that for every p ∈ (1, ∞) there exists a weight w such that the Lorentz Gamma space Γ p,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 Γ p,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 - 16 Nov 2021

Keywords

  • Lorentz Gamma space, reflexivity, Boyd indices, Zippin indices.

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