A characterization of $\dot W^{1,p}(\mathbb R^d)$

Rupert L. Frank

A characterization of $\dot W^{1,p}(\mathbb R^d)$

Functional Analysis 2022-07-12 v2 Analysis of PDEs Classical Analysis and ODEs Spectral Theory

Authors: Rupert L. Frank

Abstract

For $1<p<\infty$ we give a characterization of the Sobolev space $\dot W^{1,p}(\mathbb R^d)$ in terms of the oscillations of a function on balls of varying centers and radii. Our work is motivated both by the study of trace ideal properties of commutators with singular integral operators and by work of Nguyen and by Brezis, Van Schaftingen and Yung on derivative-free characterizations of Sobolev spaces.

Keywords

sobolev spaces

Cite

@article{arxiv.2203.01001,
  title  = {A characterization of $\dot W^{1,p}(\mathbb R^d)$},
  author = {Rupert L. Frank},
  journal= {arXiv preprint arXiv:2203.01001},
  year   = {2022}
}

Comments

16 pages; Dedicated to V. Maz'ya on the occasion of his 85th birthday; accepted version with typos corrected

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