{"paper":{"title":"Radial extensions in fractional Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haim Brezis, Itai Shafrir, Petru Mironescu","submitted_at":"2018-03-01T08:12:28Z","abstract_excerpt":"Given $f:\\partial (-1,1)^n\\to{\\mathbb R}$, consider its radial extension\n  $Tf(X):=f(X/\\|X\\|_{\\infty})$, $\\forall\\, X\\in [-1,1]^n\\setminus\\{0\\}$. In \"On some questions of topology for $S^1$-valued fractional Sobolev spaces\" (RACSAM 2001), the first two authors (HB and PM) stated the following auxiliary result (Lemma D.1). If $0<s<1$, $1< p<\\infty$ and $n\\ge 2$ are such that $1<sp<n$, then $f\\mapsto Tf$ is a bounded linear operator from $W^{s,p}(\\partial (-1,1)^n)$ into $W^{s,p}((-1,1)^n)$. The proof of this result contained a flaw detected by the third author (IS). We present a correct proof. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00241","kind":"arxiv","version":1},"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"}