English

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 BMOBMO-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}
}