{"paper":{"title":"Criteria for Optimal Global Integrability of Haj{\\l}asz-Sobolev Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Yuan Zhou","submitted_at":"2010-04-29T14:32:10Z","abstract_excerpt":"The author establishes some geometric criteria for a domain of ${\\mathbb R}^n$ with $n\\ge2$ to support a $(pn/(n-ps),\\,p)_s$-Haj{\\l}asz-Sobolev-Poincar\\'e imbedding with $s\\in(0,\\,1]$ and $p\\in(n/(n+s),\\,n/s)$ or an $s$-Haj{\\l}asz-Trudinger imbedding with $s\\in(0,\\,1]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5304","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"}