BV continuity for the uncentered Hardy--Littlewood maximal operator

preprint2020arXivOpen access

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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BV continuity for the uncentered Hardy--Littlewood maximal operator

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