{"paper":{"title":"Weighted Estimates for the iterated Commutators of Multilinear Maximal and Fractional Type Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Qingying Xue","submitted_at":"2011-05-23T11:34:16Z","abstract_excerpt":"In this paper, the following iterated commutators $T_{*,\\Pi b}$ of maximal operator for multilinear singular integral operators and $I_{\\alpha, \\Pi b}$ of multilinear fractional integral operator are introduced and studied $$\\aligned T_{*,\\Pi b}(\\vec{f})(x)&=\\sup_{\\delta>0}\\bigg|[b_1,[b_2,...[b_{m-1},[b_m,T_\\delta]_m]_{m-1}...]_2]_1 (\\vec{f})(x)\\bigg|,$$ $$\\aligned I_{\\alpha, \\Pi b}(\\vec{f})(x)&=[b_1,[b_2,...[b_{m-1},[b_m,I_\\alpha]_m]_{m-1}...]_2]_1 (\\vec{f})(x),$$ where $T_\\delta$ are the smooth truncations of the multilinear singular integral operators and $I_{\\alpha}$ is the multilinear fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4471","kind":"arxiv","version":2},"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"}