BMO-type norms and anisotropic surface measures (Q1650835)

Summary: The purpose of this note is to present an anisotropic variant of the BMO-type norm introduced in [\textit{J. Bourgain} et al., J. Eur. Math. Soc. (JEMS) 17, No. 9, 2083--2101 (2015; Zbl 1339.46028)] and to show its relation with a surface measure, which is indeed a multiple of the perimeter in the isotropic case. This is done in the spirit of the new characterization of the perimeter of a measurable set in \(\mathbb R^n\) recently studied by \textit{L. Ambrosio} et al. [Commun. Pure Appl. Math. 69, No. 6, 1062--1086 (2016; Zbl 1352.46026)].