$BMO$-type norms related to the perimeter of sets

Ambrosio Luigi - Bourgain Jean - Brezis Haim - Figalli Alessio

year: 2015
journal: Comm. Pure Appl. Math.
abstract: In this paper we consider an isotropic variant of the $BMO$-type norm recently introduced in a recent work 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.

The paper is available on the cvgmt preprint server.