{"paper":{"title":"Bilinear decompositions and commutators of singular integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Luong Dang Ky (MAPMO)","submitted_at":"2011-05-03T06:52:11Z","abstract_excerpt":"Let $b$ be a $BMO$-function. It is well-known that the linear commutator $[b, T]$ of a Calder\\'on-Zygmund operator $T$ does not, in general, map continuously $H^1(\\mathbb R^n)$ into $L^1(\\mathbb R^n)$. However, P\\'erez showed that if $H^1(\\mathbb R^n)$ is replaced by a suitable atomic subspace $\\mathcal H^1_b(\\mathbb R^n)$ then the commutator is continuous from $\\mathcal H^1_b(\\mathbb R^n)$ into $L^1(\\mathbb R^n)$. In this paper, we find the largest subspace $H^1_b(\\mathbb R^n)$ such that all commutators of Calder\\'on-Zygmund operators are continuous from $H^1_b(\\mathbb R^n)$ into $L^1(\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0486","kind":"arxiv","version":5},"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"}