JournalsrmiVol. 38, No. 3pp. 823–849

Variation of the uncentered maximal characteristic function

  • Julian Weigt

    Aalto University, Finland
Variation of the uncentered maximal characteristic function cover
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Abstract

Let M\mathrm{M} be the uncentered Hardy–Littlewood maximal operator, or the dyadic maximal operator, and let d1d\geq 1. We prove that for a set ERdE\subset\mathbb{R}^d of finite perimeter, the bound varM1ECdvar1E\operatorname{var}\mathrm{M} 1_E\leq C_d \operatorname{var} 1_E holds. We also prove this for the local maximal operator.

Cite this article

Julian Weigt, Variation of the uncentered maximal characteristic function. Rev. Mat. Iberoam. 38 (2022), no. 3, pp. 823–849

DOI 10.4171/RMI/1312