{"paper":{"title":"Trace and extension theorems for functions of bounded variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Luk\\'a\\v{s} Mal\\'y, Marie Snipes, Nageswari Shanmugalingam","submitted_at":"2015-11-14T04:20:29Z","abstract_excerpt":"In this paper we show that every $L^1$-integrable function on $\\partial\\Omega$ can be obtained as the trace of a function of bounded variation in $\\Omega$ whenever $\\Omega$ is a domain with regular boundary $\\partial\\Omega$ in a doubling metric measure space. In particular, the trace class of $BV(\\Omega)$ is $L^1(\\partial\\Omega)$ provided that $\\Omega$ supports a 1-Poincar\\'e inequality. We also construct a bounded linear extension from a Besov class of functions on $\\partial\\Omega$ to $BV(\\Omega)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04503","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"}