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arXiv · 2009.05729

BV continuity for the uncentered Hardy--Littlewood maximal operator

Cristian González-Riquelme·Dariusz Kosz
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Abstract

We prove the continuity of the map $f \mapsto \widetilde{M}f$ from $BV(\mathbb{R})$ to itself, where $\widetilde{M}$ is the uncentered Hardy--Littlewood maximal operator. This answers a question of Carneiro, Madrid and Pierce.

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Cristian González-Riquelme, Dariusz Kosz. 2020-09-12. BV continuity for the uncentered Hardy--Littlewood maximal operator. https://arxiv.org/abs/2009.05729

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