Variation of the uncentered maximal characteristic Function

2020/04/22 by Weigt, Julian · 1 citation
#26B30 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.10485

Abstract

Let \mathcal M be the uncentered Hardy-Littlewood maximal operator or the dyadic maximal operator and d≥1. We prove that for a set E⊂\mathbb R^d of finite perimeter the bound var\mathcal M1_E≤ C_dvar1_E holds. We also prove this for the local maximal operator.

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