A new characterization of Sobolev spaces on ℝ n

Roc Alabern, Joan Mateu, Joan Verdera

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33 Citations (Scopus)

Abstract

In this paper we present a new characterization of Sobolev spaces on 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 ℝ n and the Lebesgue measure, so that one can define Sobolev spaces of any order of smoothness on any metric measure space. © 2011 Springer-Verlag.
Original languageEnglish
Pages (from-to)589-626
JournalMathematische Annalen
Volume354
Issue number2
DOIs
Publication statusPublished - 1 Oct 2012

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