BMO-Type Norms Related to the Perimeter of Sets

Luigi Ambrosio, Jean Bourgain, Haim Brezis, Alessio Figalli

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In this paper we consider an isotropic variant of the BMO-type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). 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.

Original languageEnglish (US)
Pages (from-to)1062-1086
Number of pages25
JournalCommunications on Pure and Applied Mathematics
Issue number6
StatePublished - Jun 1 2016

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Mathematics(all)

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