{"paper":{"title":"Characterization of CMO via compactness of the commutators of bilinear fractional integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinghuai Wang, Jiang Zhou, Wenyi Chen","submitted_at":"2016-12-04T13:17:21Z","abstract_excerpt":"Let $I_{\\alpha}$ be the bilinear fractional integral operator, $B_{\\alpha}$ be a more singular family of bilinear fractional integral operators and $\\vec{b}=(b,b)$. B\\'{e}nyi et al. in \\cite{B1} showed that if $b\\in {\\rm CMO}$, the {\\rm BMO}-closure of $C^{\\infty}_{c}(\\mathbb{R}^n)$, the commutator $[b,B_{\\alpha}]_{i}(i=1,2)$ is a separately compact operator. In this paper, it is proved that $b\\in {\\rm CMO}$ is necessary for $[b,B_{\\alpha}]_{i}(i=1,2)$ is a compact operator. Also, the authors characterize the compactness of the {\\bf iterated} commutator $[\\Pi\\vec{b},I_{\\alpha}]$ of bilinear fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01116","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"}