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arXiv · 1509.07664

On a dual property of the maximal operator on weighted variable $L^p$ spaces

Andrei K. Lerner
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Abstract

L. Diening \cite{D1} obtained the following dual property of the maximal operator $M$ on variable Lebesque spaces $L^{p(\cdot)}$: if $M$ is bounded on $L^{p(\cdot)}$, then $M$ is bounded on $L^{p'(\cdot)}$. We extend this result to weighted variable Lebesque spaces.

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Andrei K. Lerner. 2015-09-25. On a dual property of the maximal operator on weighted variable $L^p$ spaces. https://arxiv.org/abs/1509.07664

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