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arXiv · 2608.01140

Dual boundedness of the maximal operator on concave Banach function spaces

Andrei K. Lerner
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Abstract

We prove a conjecture of Nieraeth asserting that if the Hardy--Littlewood maximal operator $M$ is bounded on an $s$-concave Banach function space $X$ for some $s\in (1,\infty)$, then $M$ is also bounded on the associate space $X'$. The proof is based on a new argument establishing the Fefferman--Stein inequality on $X$.

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BibTeXRIS

Andrei K. Lerner. 2026-08-02. Dual boundedness of the maximal operator on concave Banach function spaces. https://arxiv.org/abs/2608.01140

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