{"paper":{"title":"Weighted boundedness of the 2-fold product of Hardy-Littlewood maximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eduard Roure, Mar\\'ia J. Carro","submitted_at":"2018-01-25T08:22:51Z","abstract_excerpt":"We study new weighted estimates for the 2-fold product of Hardy-Littlewood maximal operators defined by $M^{\\otimes}(f,g):= MfMg$. This operator appears very naturally in the theory of bilinear operators such as the bilinear Calder\\'on-Zygmund operators, the bilinear Hardy-Littlewood maximal operator introduced by Calder\\'on or in the study of pseudodifferential operators. To this end, we need to study H\\\"older's inequality for Lorentz spaces with change of measures $$\n  \\Vert fg \\Vert_{L^{p,\\infty}\\left(w_1^{p/p_1} w_2^{p/p_2}\\right)} \\le C \\Vert f \\Vert_{L^{p_1,\\infty}(w_1 )} \\Vert g \\Vert_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08302","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"}