BMO-type norms related to the perimeter of sets

2014/07/08 by Luigi Ambrosio, Jean Bourgain, Ambrosio, Luigi +5 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1407.2023

arxiv created 2014/07/08 · arxiv updated 2014/07/09

Abstract

In this paper we consider an isotropic variant of the BMO-type norm recently introduced by Bourgain, Brezis and Mironescu. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.

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