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arXiv · 1808.06913

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

Alexei Yu. Karlovich
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Abstract

We show that the Hardy-Littlewood maximal operator is bounded on a reflexive variable Lebesgue space $L^{p(\cdot)}$ over a space of homogeneous type $(X,d,\mu)$ if and only if it is bounded on its dual space $L^{p'(\cdot)}$, where $1/p(x)+1/p'(x)=1$ for $x\in X$. This result extends the corresponding result of Lars Diening from the Euclidean setting of $\mathbb{R}^n$ to the setting of spaces of homogeneous type $(X,d,\mu)$.

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BibTeXRIS

Alexei Yu. Karlovich. 2018-08-16. Hardy-Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type. https://arxiv.org/abs/1808.06913

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