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arXiv · 2409.07781

On a non-standard characterization of the $A_p$ condition

Andrei K. Lerner
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Abstract

The classical Muckenhoupt's $A_p$ condition is necessary and sufficient for the boundedness of the maximal operator $M$ on $L^p(w)$ spaces. In this paper we obtain another characterization of the $A_p$ condition. As a result, we show that some strong versions of the weighted $L^p(w)$ Coifman--Fefferman and Fefferman--Stein inequalities hold if and only if $w\in A_p$. We also give new examples of Banach function spaces $X$ such that $M$ is bounded on $X$ but not bounded on the associate space $X'$.

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Andrei K. Lerner. 2024-09-12. On a non-standard characterization of the $A_p$ condition. https://arxiv.org/abs/2409.07781

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