Hardy-Littlewood maximal operator on the associate space of a Banach function space

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Abstract

Let ε(X, d, μ) be a Banach function space over a space of homogeneous type (X, d, μ). We show that if the Hardy-Littlewood maximal operator M is bounded on the space ε(X, d, μ), then its boundedness on the associate space ε'(X, d, μ) is equivalent to a certain condition A. This result extends a theorem by Andrei Lerner from the Euclidean setting of ℝn to the setting of spaces of homogeneous type.

Original languageEnglish
Pages (from-to)119-140
Number of pages22
JournalReal Analysis Exchange
Volume44
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Associate space
  • Banach function space
  • Dyadic cubes
  • Hardy-Littlewood maximal operator
  • Space of homogeneous type

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