{"paper":{"title":"Characterizations of signed measures in the dual of $BV$ and related isometric isomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Monica Torres, Nguyen Cong Phuc","submitted_at":"2015-03-20T19:54:26Z","abstract_excerpt":"We characterize all (signed) measures in $BV_{\\frac{n}{n-1}}(\\mathbb{R}^n)^*$, where $BV_{\\frac{n}{n-1}}(\\mathbb{R}^n)$ is defined as the space of all functions $u$ in $L^{\\frac{n}{n-1}}(\\mathbb{R}^n)$ such that $Du$ is a finite vector-valued measure. We also show that $BV_{\\frac{n}{n-1}}(\\mathbb{R}^n)^*$ and $BV(\\mathbb{R}^n)^*$ are isometrically isomorphic, where $BV(\\mathbb{R}^n)$ is defined as the space of all functions $u$ in $L^{1}(\\mathbb{R}^n)$ such that $Du$ is a finite vector-valued measure. As a consequence of our characterizations, an old issue raised in Meyers-Ziemer [MZ] is resol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06208","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"}