{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:WN3WHCVPS6EFZS6NBDHSIKAVDY","short_pith_number":"pith:WN3WHCVP","schema_version":"1.0","canonical_sha256":"b377638aaf97885ccbcd08cf2428151e1fbdcc6188c70892df229cbcae02ad80","source":{"kind":"arxiv","id":"2205.09851","version":1},"attestation_state":"computed","paper":{"title":"The full range of uniform bounds for the bilinear Hilbert transform","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gennady Uraltsev, Micha{\\l} Warchalski","submitted_at":"2022-05-19T20:51:05Z","abstract_excerpt":"We prove uniform uniform $L^{p}$ bounds for the family of bilinear Hilbert transforms $\\mathrm{BHT}_{\\beta} [f_1, f_2] (x) := \\mathrm{p.v.} \\int_{\\mathbb{R}} f_1 (x - t) f_2 (x + \\beta t) \\frac{\\mathrm{d} t}{t}$. We show that the operator $\\mathrm{BHT}_{\\beta}$ maps $L^{p_{1}}\\times L^{p_{2}}$ into $L^{p}$ as long as $p_1 \\in (1, \\infty)$, $p_2 \\in (1, \\infty)$, and $p > \\frac{2}{3}$ with a bound independent of $\\beta\\in(0,1]$. This is the full open range of exponents where the modulation invariant class of bilinear operators containing $\\mathrm{BHT}_{\\beta}$ can be bounded uniformly. This is "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2205.09851","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2022-05-19T20:51:05Z","cross_cats_sorted":[],"title_canon_sha256":"e427ed34920af64a08c770364ea23ac06463a1e9cd06c49712879f09ee9db816","abstract_canon_sha256":"75c000e90ac418f11ef1f42e55f3a24d5a9b2670a796b5162e5a1e1e419c298a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:25:00.968733Z","signature_b64":"dtULL9fW9Aw2jWM4wQ6+eY6UfW7ML9oL/mbHAXuBgyq7PlEWaQKqGmpIwtU5IEeBZCe9PZt+2F3ZipBObXRFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b377638aaf97885ccbcd08cf2428151e1fbdcc6188c70892df229cbcae02ad80","last_reissued_at":"2026-07-05T04:25:00.968282Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:25:00.968282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The full range of uniform bounds for the bilinear Hilbert transform","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gennady Uraltsev, Micha{\\l} Warchalski","submitted_at":"2022-05-19T20:51:05Z","abstract_excerpt":"We prove uniform uniform $L^{p}$ bounds for the family of bilinear Hilbert transforms $\\mathrm{BHT}_{\\beta} [f_1, f_2] (x) := \\mathrm{p.v.} \\int_{\\mathbb{R}} f_1 (x - t) f_2 (x + \\beta t) \\frac{\\mathrm{d} t}{t}$. We show that the operator $\\mathrm{BHT}_{\\beta}$ maps $L^{p_{1}}\\times L^{p_{2}}$ into $L^{p}$ as long as $p_1 \\in (1, \\infty)$, $p_2 \\in (1, \\infty)$, and $p > \\frac{2}{3}$ with a bound independent of $\\beta\\in(0,1]$. This is the full open range of exponents where the modulation invariant class of bilinear operators containing $\\mathrm{BHT}_{\\beta}$ can be bounded uniformly. This is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.09851","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/2205.09851/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2205.09851","created_at":"2026-07-05T04:25:00.968351+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.09851v1","created_at":"2026-07-05T04:25:00.968351+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.09851","created_at":"2026-07-05T04:25:00.968351+00:00"},{"alias_kind":"pith_short_12","alias_value":"WN3WHCVPS6EF","created_at":"2026-07-05T04:25:00.968351+00:00"},{"alias_kind":"pith_short_16","alias_value":"WN3WHCVPS6EFZS6N","created_at":"2026-07-05T04:25:00.968351+00:00"},{"alias_kind":"pith_short_8","alias_value":"WN3WHCVP","created_at":"2026-07-05T04:25:00.968351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY","json":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY.json","graph_json":"https://pith.science/api/pith-number/WN3WHCVPS6EFZS6NBDHSIKAVDY/graph.json","events_json":"https://pith.science/api/pith-number/WN3WHCVPS6EFZS6NBDHSIKAVDY/events.json","paper":"https://pith.science/paper/WN3WHCVP"},"agent_actions":{"view_html":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY","download_json":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY.json","view_paper":"https://pith.science/paper/WN3WHCVP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.09851&json=true","fetch_graph":"https://pith.science/api/pith-number/WN3WHCVPS6EFZS6NBDHSIKAVDY/graph.json","fetch_events":"https://pith.science/api/pith-number/WN3WHCVPS6EFZS6NBDHSIKAVDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY/action/storage_attestation","attest_author":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY/action/author_attestation","sign_citation":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY/action/citation_signature","submit_replication":"https://pith.science/pith/WN3WHCVPS6EFZS6NBDHSIKAVDY/action/replication_record"}},"created_at":"2026-07-05T04:25:00.968351+00:00","updated_at":"2026-07-05T04:25:00.968351+00:00"}