Addendum to "The Kolmogorov--Riesz compactness theorem" (Expo. Math. 28:385--394 (2010))

Harald Hanche-Olsen; Helge Holden

doi:10.1016/j.exmath.2015.12.003

Addendum to "The Kolmogorov--Riesz compactness theorem" (Expo. Math. 28:385--394 (2010))

Classical Analysis and ODEs 2016-05-31 v2

Authors: Harald Hanche-Olsen , Helge Holden

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Abstract

We show how to improve on Theorem 10 in [arXiv:0906.4883], describing when subsets in $W^{1,p}(\mathbb{R}^n)$ are totally bounded subsets of $L^q(\mathbb{R}^n)$ for $p<n$ and $p\le q<p^*$ . This improvement was first shown by Dosso, Fofana, and Sanogo (2013) in the context of Morrey--Sobolov spaces.

Keywords

Kolmogorov-Riesz theorem compactness theorem totally bounded Sobolev space Morrey-Sobolev space

Cite

@article{arxiv.1508.07892,
  title  = {Addendum to "The Kolmogorov--Riesz compactness theorem" (Expo. Math. 28:385--394 (2010))},
  author = {Harald Hanche-Olsen and Helge Holden},
  journal= {arXiv preprint arXiv:1508.07892},
  year   = {2016}
}

Comments

2 pages. This is an addendum to our paper arXiv:0906.4883 . To appear in Expo. Math. Revision 2 fixes a minor mistake in the final estimate (pointed out by the referee)

Addendum to "The Kolmogorov--Riesz compactness theorem" (Expo. Math. 28:385--394 (2010))

Abstract

Keywords

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