{"paper":{"title":"Rough Bilinear Singular Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Danqing He, Loukas Grafakos, Petr Honz\\'ik","submitted_at":"2015-09-21T03:03:38Z","abstract_excerpt":"We study the rough bilinear singular integral, introduced by Coifman and Meyer , $$ T_\\Omega(f,g)(x)=p.v. \\! \\int_{\\mathbb R^{n}}\\! \\int_{\\mathbb R^{n}}\\! |(y,z)|^{-2n} \\Omega((y,z)/|(y,z)|)f(x-y)g(x-z) dydz, $$ when $\\Omega $ is a function in $L^q(\\mathbb S^{2n-1})$ with vanishing integral and $2\\le q\\le \\infty$. When $q=\\infty$ we obtain boundedness for $T_\\Omega$ from $L^{p_1}(\\mathbb R^n)\\times L^{p_2}(\\mathbb R^n)$ to $ L^p(\\mathbb R^n) $ when $1<p_1, p_2<\\infty$ and $1/p=1/p_1+1/p_2$. For $q=2$ we obtain that $T_\\Omega$ is bounded from $L^{2}(\\mathbb R^n)\\times L^{ 2}(\\mathbb R^n)$ to $ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06099","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"}