{"paper":{"title":"Weighted Estimates for Rough Bilinear Singular Integrals via Sparse Domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Barron","submitted_at":"2017-02-15T21:45:35Z","abstract_excerpt":"We prove weighted estimates for rough bilinear singular integral operators with kernel $$K(y_1, y_2) = \\frac{\\Omega((y_1,y_2)/|(y_1,y_2)|)}{|(y_1, y_2)|^{2d}},$$ where $y_i \\in \\mathbb{R}^{d}$ and $\\Omega \\in L^{\\infty}(S^{2d-1})$ with $\\int_{S^{2d-1}}\\Omega d\\sigma = 0.$ The argument is by sparse domination of rough bilinear operators, via an abstract theorem that is a multilinear generalization of recent work by Conde-Alonso, Culiuc, Di Plinio and Ou. We also use recent results due to Grafakos, He, and Honz\\'{\\i}k for the application to rough bilinear operators. In particular, since the weig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04790","kind":"arxiv","version":3},"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"}