{"paper":{"title":"Endpoint bounds for the bilinear Hilbert transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Christoph Thiele, Francesco Di Plinio","submitted_at":"2014-03-24T14:51:22Z","abstract_excerpt":"We study the behavior of the bilinear Hilbert transform $\\mathrm{BHT}$ at the boundary of the known boundedness region $\\mathcal H$. A sample of our results is the estimate\n  $| \\langle\\mathrm{BHT}(f_1,f_2),f_3 \\rangle | \\leq C |F_1|^{\\frac34}|F_2| ^{\\frac34} |F_3|^{-\\frac12} \\log\\log \\Big(\\mathrm{e}^{\\mathrm{e}} + \\frac{|F_3|}{\\min\\{|F_1|,|F_2|\\}} \\Big) $  valid for all tuples of sets $F_j \\subset \\mathbb R $ of finite measure and functions $f_j$ such that $|f_j| \\leq \\mathbf{1}_{F_j}$, $j=1,2,3$, with the additional restriction that $f_3$ be supported on a major subset $F_3'$ of $F_3$ that d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5978","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"}