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arXiv · 2603.09388

The maximal operator on variable Lebesgue spaces: an ${\mathcal A}_{\infty}$-characterization

Andrei K. Lerner
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Abstract

In this paper we obtain a new boundedness criterion for the maximal operator $M$ on variable exponent spaces $L^{p(\cdot)}$. It is formulated in terms of the variable exponent analogue of the well known weighted $A_{\infty}$ condition.

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Andrei K. Lerner. 2026-03-10. The maximal operator on variable Lebesgue spaces: an ${\mathcal A}_{\infty}$-characterization. https://arxiv.org/abs/2603.09388

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