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

Alexei Karlovich

doi:10.4064/sm180816-16-9

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

Alexei Karlovich

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Abstract

We show that the Hardy–Littlewood maximal operator is bounded on a reflexive variable Lebesgue space L^p(·) over a space of homogeneous type (X, d, µ) if and only if it is bounded on its dual space L^p0(·), 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 language	English
Pages (from-to)	149-178
Number of pages	30
Journal	Studia Mathematica
Volume	254
Issue number	2
DOIs	https://doi.org/10.4064/sm180816-16-9
Publication status	Published - 2020

Keywords

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

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10.4064/sm180816-16-9

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

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