{"paper":{"title":"Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cornelia Schneider, Jan Vyb\\'iral","submitted_at":"2012-01-11T11:14:50Z","abstract_excerpt":"We provide non-smooth atomic decompositions for Besov spaces $\\Bd(\\rn)$, $s>0$, $0<p,q\\leq \\infty$, defined via differences. The results are used to compute the trace of Besov spaces on the boundary $\\Gamma$ of bounded Lipschitz domains $\\Omega$ with smoothness $s$ restricted to $0<s<1$ and no further restrictions on the parameters $p,q$. We conclude with some more applications in terms of pointwise multipliers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2280","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"}