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arXiv · 1508.07892

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

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.

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Harald Hanche-Olsen, Helge Holden. 2015-08-31. Addendum to "The Kolmogorov--Riesz compactness theorem" (Expo. Math. 28:385--394 (2010)). https://doi.org/10.1016/j.exmath.2015.12.003

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