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

Roc Alabern; Joan Mateu; Joan Verdera

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

Classical Analysis and ODEs 2010-11-30 v2 Analysis of PDEs Functional Analysis

Authors: Roc Alabern , Joan Mateu , Joan Verdera

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.

Keywords

Sobolev spaces new characterization quadratic multiscale expression Euclidean space metric measure space

Cite

@article{arxiv.1011.0667,
  title  = {A new characterization of Sobolev spaces on $\mathbb{R}^n$},
  author = {Roc Alabern and Joan Mateu and Joan Verdera},
  journal= {arXiv preprint arXiv:1011.0667},
  year   = {2010}
}

Comments

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

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

Abstract

Keywords

Cite

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