{"paper":{"title":"The Structure of Sobolev Extension 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":"2012-06-09T22:59:12Z","abstract_excerpt":"Let $L^{m,p}(\\R^n)$ denote the Sobolev space of functions whose $m$-th derivatives lie in $L^p(\\R^n)$, and assume that $p>n$. For $E \\subset \\R^n$, denote by $L^{m,p}(E)$ the space of restrictions to $E$ of functions $F \\in L^{m,p}(\\R^n)$. It is known that there exist bounded linear maps $T : L^{m,p}(E) \\rightarrow L^{m,p}(\\R^n)$ such that $Tf = f$ on $E$ for any $f \\in L^{m,p}(E)$. We show that $T$ cannot have a simple form called \"bounded depth.\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1979","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"}