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It is conjectured that $H_k$ maps $L^{p_1}({\\bf R}) \\times \\dots \\times L^{p_k}({\\bf R}) \\to L^p({\\bf R})$ whenever $1 < p_1,\\dots,p_k,p < \\infty$ and $\\frac{1}{p} = \\frac{1}{p_1} + \\dots + \\frac{1}{p_k}$. This is proven for $k=1,2$, but remains open for larger $k$.\n  In this paper, we consider the truncated operators $$ H_{k,r,R}( f_1,\\dots,f_k )(x) := \\int_{r \\leq ","authors_text":"Terence Tao","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-24T20:49:18Z","title":"Cancellation for the multilinear Hilbert transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06479","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e2709b5d8d2d976ffa5a317c54312448d30795f8df72a6431309f6cbb428b042","target":"record","created_at":"2026-05-18T02:00:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3e91031e3cbc85c5d2e6fa00358d9058d977b7c157c1c389e0ab529e1f8a1269","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-24T20:49:18Z","title_canon_sha256":"5db45b942d1581cb9e8ee4dab1bc9cbd7728df9aeea9cca00918c0a340564f0e"},"schema_version":"1.0","source":{"id":"1505.06479","kind":"arxiv","version":3}},"canonical_sha256":"be264bbeecb65bdc45e87296b7374153d4975a45de03f8b335603b352a81f70d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be264bbeecb65bdc45e87296b7374153d4975a45de03f8b335603b352a81f70d","first_computed_at":"2026-05-18T02:00:01.876851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:01.876851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9aYQQhLH506CDf+6J/URSJUtMJ5fgkR7t3l53/wZsoFvmdUWNAXgSfp889R2Fu1WxjfOWqPT4wCRJURMGv08Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:01.877275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06479","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2709b5d8d2d976ffa5a317c54312448d30795f8df72a6431309f6cbb428b042","sha256:4660846feab5276a5212eb490d03c7f88f9da4559b5e93d8ee5487eebe713b61"],"state_sha256":"ceec6183ace61a33f588d99876c9eef0fe11cb87faa6f50c2d755f2109470f54"}