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Define a model bilinear generalized Radon transform, $$B_{\\theta}(f,g)(x)=\\int_{S^1} f(x-y)g(x-\\Theta y)\\, d\\sigma(y),$$ an analogue of the linear generalized Radon transforms of Guillemin and Sternberg \\cite{GS} and Phong and Stein (e.g., \\cite{PhSt91,St93}). Operators such as $B_\\theta$ are motivated by problems in geometric measure theory and combinatorics. For $\\theta<\\pi$, we show that $B_{\\theta}: L^p({\\Bbb R}^2) \\times L^q({\\Bbb R}^2) \\to L^r({\\Bbb R}^2)$ if $\\l"},"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":"1704.00861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-04T03:07:21Z","cross_cats_sorted":[],"title_canon_sha256":"79be2213849ace3da8382521908467259782d66853f25fd07d4561b14b87a425","abstract_canon_sha256":"51f3b8288ae13f522577df6ee50bee8ab82a6bb42b056a158e828372006f5854"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:19.021643Z","signature_b64":"MBGUlOS2lH7JOV0toytiVza/ao3QxwQ7oVXzQYHpXd2aVgvTM/tftZPjKKOrmXiLzv4N2Yd0UrKRle0Wj++3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"067e1e559ed5a81546879fa9d2405f8bb3d1e66eeb6f154c24f7df3572eb9bfa","last_reissued_at":"2026-05-18T00:47:19.020907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:19.020907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bilinear generalized Radon transforms in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Allan Greenleaf, Allen Liu, Ben Krause","submitted_at":"2017-04-04T03:07:21Z","abstract_excerpt":"Let $\\sigma$ be arc-length measure on $S^1\\subset \\mathbb R^2$ and $\\Theta$ denote rotation by an angle $\\theta \\in (0, \\pi]$. Define a model bilinear generalized Radon transform, $$B_{\\theta}(f,g)(x)=\\int_{S^1} f(x-y)g(x-\\Theta y)\\, d\\sigma(y),$$ an analogue of the linear generalized Radon transforms of Guillemin and Sternberg \\cite{GS} and Phong and Stein (e.g., \\cite{PhSt91,St93}). Operators such as $B_\\theta$ are motivated by problems in geometric measure theory and combinatorics. 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