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

2018/08/16 by Karlovich, Alexei Yu. · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.06913

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^p'(⋅), where 1/p(x)+1/p'(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 of homogeneous type (X,d,μ).

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