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arXiv · 2109.09691

Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level

Cristian González-Riquelme
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Abstract

We prove the continuity of the map $f \mapsto (Mf)'$ from $W^{1,1}(\mathbb{R})$ to $L^1(\mathbb{R})$, where $M$ is the centered Hardy-Littlewood maximal operator. This solves a question posed by Carneiro, Madrid and Pierce.

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Cristian González-Riquelme. 2021-09-20. Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level. https://arxiv.org/abs/2109.09691

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