{"paper":{"title":"Intrinsic atomic characterization of 2-microlocal spaces with variable exponents on domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Helena F. Gon\\c{c}alves, Henning Kempka","submitted_at":"2016-07-20T09:30:36Z","abstract_excerpt":"We provide an intrinsic atomic characterization for 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability on domains, $B_{\\p,\\q}^{\\bm{w}}(\\Omega)$ and $F_{\\p,\\q}^{\\bm{w}}(\\Omega)$, where $\\Omega$ is a regular domain. We use the already known decomposition with non-smooth atoms for the spaces $B_{\\p,\\q}^{\\bm{w}}(\\rn)$ and $F_{\\p,\\q}^{\\bm{w}}(\\rn)$ in order to get the main result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05885","kind":"arxiv","version":3},"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"}