{"paper":{"title":"Two weight norm inequalities for the bilinear fractional integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kangwei Li, Wenchang Sun","submitted_at":"2013-12-30T13:21:40Z","abstract_excerpt":"In this paper, we give a characterization of the two weight strong and weak type norm inequalities for the bilinear fractional integrals. Namely, we give the characterization of the following inequalities, \\[\n  \\|\\mathcal I_\\alpha (f_1\\sigma_1, f_2\\sigma_2)\\|_{L^q(w)} \\le \\mathscr N \\prod_{i=1}^2\\|f_i\\|_{L^{p_i}(\\sigma_i)} \\] and \\[\n  \\|\\mathcal I_\\alpha (f_1\\sigma_1, f_2\\sigma_2)\\|_{L^{q,\\infty}(w)} \\le \\mathscr N_{\\textup{weak}} \\prod_{i=1}^2\\|f_i\\|_{L^{p_i}(\\sigma_i)}, \\] when $q\\ge p_1, p_2>1$ and $p_1+p_2\\ge p_1p_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7707","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"}