{"paper":{"title":"Addendum to \"The Kolmogorov--Riesz compactness theorem\" (Expo. Math. 28:385--394 (2010))","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Harald Hanche-Olsen, Helge Holden","submitted_at":"2015-08-31T16:18:40Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07892","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}