Roc Alabern scite author profile

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.

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

Alabern¹,

Mateu²,

Verdera³

2010

Preprint

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Roc Alabern

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

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

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