BMO-type norms related to the perimeter of sets
Functional Analysis
2014-07-09 v1
Abstract
In this paper we consider an isotropic variant of the -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.
Keywords
Cite
@article{arxiv.1407.2023,
title = {BMO-type norms related to the perimeter of sets},
author = {Luigi Ambrosio and Jean Bourgain and Haim Brezis and Alessio Figalli},
journal= {arXiv preprint arXiv:1407.2023},
year = {2014}
}