{"paper":{"title":"Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jianglong Wu, Qingguo Liu","submitted_at":"2013-04-16T13:15:43Z","abstract_excerpt":"Let $\\mu_{\\Omega,\\vec{b}}$ be the multilinear commutator generalized by $\\mu_{\\Omega}$, the $n$-dimensional Marcinkiewicz integral, with $\\Osc_{\\exp L^{^{\\tau}}}(\\R^{n})$ functions for $\\tau\\ge 1$, where $\\Osc_{\\exp L^{^{\\tau}}}(\\R^{n})$ is a space of Orlicz type satisfying that $\\Osc_{\\exp L^{^{\\tau}}}(\\R^{n})=\\BMO(\\R^{n})$ if $\\tau=1$ and $\\Osc_{\\exp L^{^{\\tau}}}(\\R^{n})\\subset\\BMO(\\R^{n})$ if $\\tau>1$. The authors establish the weighted weak $L\\log L$-type estimates for $\\mu_{\\Omega,\\vec{b}}$ when $\\Omega$ satisfies a kind of Dini conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4431","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"}