{"paper":{"title":"On the extension of VMO functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Almaz Butaev, Galia Dafni","submitted_at":"2018-09-04T15:37:19Z","abstract_excerpt":"We consider functions of vanishing mean oscillation on a bounded domain $\\Omega$ and prove a $\\rm{VMO}$ analogue of the extension theorem of P. Jones for $\\rm{BMO}(\\Omega)$. We show that if $\\Omega$ satisfies the same condition imposed by Jones (i.e.\\ is a uniform domain), there is a linear extension map from $\\rm{VMO}(\\Omega)$ to $\\rm{VMO}(\\mathbb{R}^n)$ which is bounded in the $\\rm{BMO}$ norm. Moreover, if such an extension map exists from $\\rm{VMO}(\\Omega)$ to $\\rm{BMO}(\\mathbb{R}^n)$, then the domain is uniform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01049","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"}