{"paper":{"title":"Sharp estimates for commutators of bilinear operators on Morrey type spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinghuai Wang, Jiang Zhou, Zhidong Teng","submitted_at":"2017-03-19T06:38:49Z","abstract_excerpt":"Denote by $T$ and $I_{\\alpha}$ the bilinear Calder\\'{o}n-Zygmund operators and bilinear fractional integrals, respectively. In this paper, it is proved that if $b_{1},b_{2}\\in {\\rm CMO}$ (the {\\rm BMO}-closure of $C^{\\infty}_{c}(\\mathbb{R}^n)$), $[\\Pi \\vec{b},T]$ and $[\\Pi\\vec{b},I_{\\alpha}]$ $(\\vec{b}=(b_{1},b_{2}))$ are all the compact operators from $\\mathcal{M}^{p_{0}}_{\\vec{P}}$ (the norm of $\\mathcal{M}^{p_{0}}_{\\vec{P}}$ is strictly smaller than $2-$fold product of the Morrey norms) to $M^{q_{0}}_{q}$ for some suitable indexes $p_{0},p_{1},p_{2}$ and $q_{0},q$. Specially, we also show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06395","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"}