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arXiv · 2609.12440

The norm of the centered Hardy--Littlewood maximal operator

José Madrid
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Abstract

We determine the exact $L^p(\mathbb{R})$ norm of the centered Hardy--Littlewood maximal operator for every $1<p<\infty$, proving that it equals $p/(p-1)$. This settles the sharp strong-type problem for the centered maximal operator on the real line. For every $p$ in this range, the norm is strictly larger than the constant associated with the critical power $|x|^{-1/p}$, thereby disproving the conjecture of Dror, Ganguli, and Strichartz that this profile determines the unrestricted norm.

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José Madrid. 2026-09-11. The norm of the centered Hardy--Littlewood maximal operator. https://arxiv.org/abs/2609.12440

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