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arXiv · 2601.19272

On an improved restricted reverse weak-type bound for the maximal operator

Andrei K. Lerner
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Abstract

We obtain an improved lower bound for the restricted reverse weak-type estimate of the Hardy-Littlewood maximal operator $M$. This result is applied to the $\lambda$-median maximal operator $m_{\lambda}$ acting on a Banach function space $X$. We show that under certain assumptions on $X$, the boundedness properties of $m_{\lambda}$ and $M$ are equivalent.

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Andrei K. Lerner. 2026-01-27. On an improved restricted reverse weak-type bound for the maximal operator. https://arxiv.org/abs/2601.19272

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