{"paper":{"title":"Bilinear singular integral operators with kernels in weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lenka Slav\\'ikov\\'a, Petr Honz\\'ik, Stefanos Lappas","submitted_at":"2024-12-09T21:45:22Z","abstract_excerpt":"We establish the full quasi-Banach range of $L^{p_1}(\\mathbb R) \\times L^{p_2}(\\mathbb R) \\rightarrow L^p(\\mathbb R)$ bounds for one-dimensional bilinear singular integral operators with homogeneous kernels whose restriction $\\Omega$ to the unit sphere $\\mathbb S^1$ is supported away from the degenerate line $\\theta_1=\\theta_2$, belongs to $L^q(\\mathbb S^1)$ for some $q>1$ and has vanishing integral. In fact, a more general result is obtained by dropping the support condition on $\\Omega$ and requiring that $\\Omega\\in L^q(\\mathbb S^1,u^q)$, where $u(\\theta_1,\\theta_2)=|\\theta_1-\\theta_2|^{-1}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.07014","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.07014/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"}