{"paper":{"title":"Extension of Multilinear Fractional Integral Operators to Linear Operators on Lebesgue Spaces with Mixed Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ting Chen, Wenchang Sun","submitted_at":"2019-02-12T18:07:26Z","abstract_excerpt":"In [C. E. Kenig and E. M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett., 6(1):1-15, 1999], the following type of multilinear fractional integral \\[\n  \\int_{\\mathbb{R}^{mn}} \\frac{f_1(l_1(x_1,\\ldots,x_m,x))\\cdots f_{m+1}(l_{m+1}(x_1,\\ldots,x_m,x))}{(|x_1|+\\ldots+|x_m|)^{\\lambda}} dx_1\\ldots dx_m \\] was studied, where $l_i$ are linear maps from $\\mathbb{R}^{(m+1)n}$ to $\\mathbb{R}^n$ satisfying certain conditions. They proved the boundedness of such multilinear fractional integral from $L^{p_1}\\times \\ldots \\times L^{p_{m+1}}$ to $L^q$ when the indices satisfy the hom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04527","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.04527/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}