Variation of the uncentered maximal characteristic function

Variation of the uncentered maximal characteristic function

Let \mathrm{M} be the uncentered Hardy–Littlewood maximal operator, or the dyadic maximal operator, and let d\geq 1 . We prove that for a set E\subset\mathbb{R}^d of finite perimeter, the bound \operatorname{var}\mathrm{M} 1_E\leq C_d \operatorname{var} 1_E holds. We also prove this for the local ma...

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Veröffentlicht in:Revista matemática iberoamericana 2022-05, Vol.38 (3), p.823-849
1. Verfasser: Weigt, Julian
Format: Artikel
Sprache:eng
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Zusammenfassung:Let \mathrm{M} be the uncentered Hardy–Littlewood maximal operator, or the dyadic maximal operator, and let d\geq 1 . We prove that for a set E\subset\mathbb{R}^d of finite perimeter, the bound \operatorname{var}\mathrm{M} 1_E\leq C_d \operatorname{var} 1_E holds. We also prove this for the local maximal operator.
ISSN:0213-2230
2235-0616
DOI:10.4171/RMI/1312