Revista de la
Unión Matemática Argentina
On a non-standard characterization of the $A_p$ condition
Andrei K. Lerner

Volume 68, no. 2 (2025), pp. 691–701    

Published online (final version): October 8, 2025

https://doi.org/10.33044/revuma.4964

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Abstract

The classical Muckenhoupt $A_p$ 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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