{"paper":{"title":"The Bilinear Hilbert-Carleson operator along curves. The purely non-zero curvature case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.CA","authors_text":"\\'Arp\\'ad B\\'enyi, Bingyang Hu, Victor Lie","submitted_at":"2025-07-06T17:11:44Z","abstract_excerpt":"In this paper, we provide the maximal boundedness range (up to end-points) for the Bilinear Hilbert-Carleson operator along curves in the (purely) non-zero curvature setting. More precisely, we show that the operator $$ BHC_{[\\vec{a},\\vec{\\alpha}]}(f_1,f_2)(x) := \\sup_{\\lambda\\in\\mathbb{R}} \\left|\\,p.v.\\, \\int_{\\mathbb{R}} f_1(x - a_1 t^{\\alpha_1}) \\,f_2(x - a_2 t^{\\alpha_2}) \\,e^{i\\,\\lambda\\,a_3 \\,t^{\\alpha_3}} \\,\\frac{dt}{t}\\right|$$ obeys the bounds $$\\|BHC_{[\\vec{a},\\vec{\\alpha}]} (f_1,f_2)\\|_{L^r} \\lesssim_{\\vec{a} \\,\\vec{\\alpha},r,p_1,p_2} \\|f_1\\|_{L^{p_1}}\\,\\|f_2\\|_{L^{p_2}}$$ whenever "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04467","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.04467/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"}