{"paper":{"title":"Morrey-Sobolev Spaces on Metric Measure Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Wen Yuan, Yufeng Lu","submitted_at":"2013-04-14T02:15:55Z","abstract_excerpt":"In this article, the authors introduce the Newton-Morrey-Sobolev space on a metric measure space $(\\mathscr{X},d,\\mu)$. The embedding of the Newton-Morrey-Sobolev space into the H\\\"older space is obtained if $\\mathscr{X}$ supports a weak Poincar\\'e inequality and the measure $\\mu$ is doubling and satisfies a lower bounded condition. Moreover, in the Ahlfors $Q$-regular case, a Rellich-Kondrachov type embedding theorem is also obtained. Using the Haj{\\l}asz gradient, the authors also introduce the Haj{\\l}asz-Morrey-Sobolev spaces, and prove that the Newton-Morrey-Sobolev space coincides with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3871","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"}