%0 Journal Article
%T A new characterization of Sobolev spaces on $\mathbb{R}^n$
%A Roc Alabern
%A Joan Mateu
%A Joan Verdera
%J Mathematics
%D 2010
%I arXiv
%X In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of Euclidean space. An interesting feature of our condition is that depends only on the metric of $\mathbb{R}^n$ and the Lebesgue measure, so that one can define Sobolev spaces of any order of smoothness on any metric measure space.
%U http://arxiv.org/abs/1011.0667v2