$BMO$-type norms related to the perimeter of sets
Comm. Pure Appl. Math.
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
The paper is available on the
cvgmt preprint server.