Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type

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Abstract

We show that the Hardy–Littlewood maximal operator is bounded on a reflexive variable Lebesgue space Lp(·) over a space of homogeneous type (X, d, µ) if and only if it is bounded on its dual space Lp0(·), where 1/p(x) + 1/p0(x) = 1 for x ∈ X. This result extends the corresponding result of Lars Diening from the Euclidean setting of Rn to the setting of spaces (X, d, µ) of homogeneous type.

Original languageEnglish
Pages (from-to)149-178
Number of pages30
JournalStudia Mathematica
Volume254
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Dyadic cubes
  • Hardy–Littlewood maximal operator
  • Space of homogeneous type
  • Variable Lebesgue space

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