{"paper":{"title":"Weak and Strong Type Weighted Estimates for Multilinear Calder\\'{o}n-Zygmund Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kangwei Li, Wenchang Sun","submitted_at":"2012-12-17T14:47:32Z","abstract_excerpt":"In this paper, we study the weighted estimates for multilinear Calder\\'{o}n-Zygmund operators %with multiple $A_{\\vec{P}}$ weights from $L^{p_1}(w_1)\\times...\\times L^{p_m}(w_m)$ to $L^{p}(v_{\\vec{w}})$, where $1<p, p_1,...,p_m<\\infty$ with $1/{p_1}+...+1/{p_m}=1/p$ and $\\vec{w}=(w_1,...,w_m)$ is a multiple $A_{\\vec{P}}$ weight. We give weak and strong type weighted estimates of mixed $A_p$-$A_\\infty$ type. Moreover, the strong type weighted estimate is sharp whenever $\\max_i p_i \\le p'/(mp-1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4011","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"}