{"paper":{"title":"On the Boundedness of Multilinear Fractional Strong Maximal Operator with multiple weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Kozo Yabuta, Mingming Cao, Qingying Xue","submitted_at":"2015-12-29T13:43:55Z","abstract_excerpt":"In this paper, we investigated the boundedness of multilinear fractional strong maximal operator $\\mathcal{M}_{\\mathcal{R},\\alpha}$ associated with rectangles or related to more general basis with multiple weights $A_{(\\vec{p},q),\\mathcal{R}}$. In the rectangles setting, we first gave an end-point estimate of $\\mathcal{M}_{\\mathcal{R},\\alpha}$, which not only extended the famous linear result of Jessen, Marcinkiewicz and Zygmund, but also extended the multilinear result of Grafakos, Liu, P\\'{e}rez and Torres ($\\alpha=0$) to the case $0<\\alpha<mn.$ Then, in one weight case, we gave several equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08681","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"}