{"paper":{"title":"Sobolev Extension By Linear Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arie Israel, Charles L. Fefferman, Garving K. Luli","submitted_at":"2012-05-11T13:57:44Z","abstract_excerpt":"Let $L^{m,p}(\\R^n)$ be the Sobolev space of functions with $m^{th}$ derivatives lying in $L^p(\\R^n)$. Assume that $n< p < \\infty$. For $E \\subset \\R^n$, let $L^{m,p}(E)$ denote the space of restrictions to $E$ of functions in $L^{m,p}(\\R^n)$. We show that there exists a bounded linear map $T : L^{m,p}(E) \\rightarrow L^{m,p}(\\R^n)$ such that, for any $f \\in L^{m,p}(E)$, we have $Tf = f$ on $E$. We also give a formula for the order of magnitude of $\\|f\\|_{L^{m,p}(E)}$ for a given $f : E \\rightarrow \\R$ when $E$ is finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2525","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"}