{"paper":{"title":"Improved bound for the bilinear Bochner-Riesz operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ana Vargas, Eunhee Jeong, Sanghyuk Lee","submitted_at":"2017-11-07T12:06:30Z","abstract_excerpt":"We study $L^p\\times L^q\\to L^r$ bounds for the bilinear Bochner-Riesz operator $\\mathcal{B}^\\alpha$, $\\alpha>0$ in $\\mathbb{R}^d,$ $d\\ge2$, which is defined by \\[ {\\mathcal B}^{\\alpha}(f,g)=\\iint_{\\mathbb{R}^d\\times\\mathbb{R}^d} e^{2\\pi i x\\cdot(\\xi+\\eta)} (1-|\\xi|^2-|\\eta|^2 )^{\\alpha}_+ ~ \\widehat{f}(\\xi)\\,\\widehat{g}(\\eta)\\,d\\xi d\\eta.\\] We make use of a decomposition which relates the estimates for $\\mathcal{B}^\\alpha$ to those of the square function estimates for the classical Bochner-Riesz operators. In consequence, we significantly improve the previously known bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02425","kind":"arxiv","version":1},"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"}