A new characterization of Sobolev spaces on $\mathbb{R}^n$

Details A new characterization of Sobolev spaces on $\mathbb{R}^n$ A new characterization of Sobolev spaces on $\mathbb{R}^n$

2010-11-02

arxiv.org/abs/1011.0667v2

Mathematics

Classical Analysis and ODEs

Two references added. Some statements have been improved and proofs made clearer. Typos corrected

Scientific paper

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.

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