BMO-type norms related to the perimeter of sets
Luigi Ambrosio, Jean Bourgain, Haim Brezis, Alessio Figalli
TL;DR
This paper introduces an isotropic BMO-type norm related to set perimeters, providing a new characterization of perimeter that does not rely on distribution theory.
Contribution
It establishes a novel connection between an isotropic BMO-type norm and the perimeter of sets, offering an alternative characterization independent of distributions.
Findings
Norm is related to the perimeter of sets
Provides a new perimeter characterization
Independent of distribution theory
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.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Banach Space Theory · Mathematical Analysis and Transform Methods