{"paper":{"title":"Compactness of commutators of bilinear maximal Calder\\'{o}n-Zygmund singular integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Qingying Xue, Ting Mei, Yong Ding","submitted_at":"2013-10-22T03:12:51Z","abstract_excerpt":"Let $T$ be a bilinear Calder\\'{o}n-Zygmund singular integral operator and $T_*$ be its corresponding truncated maximal operator. The commutators in the $i$-$th$ entry and the iterated commutators of $T_*$ are defined by $$ T_{\\ast,b,1}(f,g)(x)=\\sup_{\\delta>0}\\bigg|\\iint_{|x-y|+|x-z|>\\delta}K(x,y,z)(b(y)-b(x))f(y)g(z)dydz\\bigg|, $$ $$T_{\\ast,b,2}(f,g)(x)=\\sup_{\\delta>0}\\bigg|\\iint_{|x-y|+|x-z|>\\delta}K(x,y,z)(b(z)-b(x))f(y)g(z)dydz\\bigg|,$$ \\begin{align*} T_{\\ast,(b_1,b_2)}(f,g)(x)=\\sup\\limits_{\\delta>0}\\bigg|\\iint_{|x-y|+|x-z|>\\delta} K(x,y,z)(b_1(y)-b_1(x))(b_2(z)-b_2(x))f(y)g(z)dydz\\bigg|. \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5787","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"}