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

Roc Alabern; Joan Mateu; Joan Verdera

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arXiv · 1011.0667

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

Roc Alabern·Joan Mateu·Joan Verdera

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Abstract

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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BibTeX RIS

Roc Alabern, Joan Mateu, Joan Verdera. 2010-11-27. A new characterization of Sobolev spaces on $\mathbb{R}^n$. https://arxiv.org/abs/1011.0667

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