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Stein","submitted_at":"2011-05-23T19:31:25Z","abstract_excerpt":"The goal of this paper is to study operators of the form, \\[ Tf(x)= \\psi(x)\\int f(\\gamma_t(x))K(t)\\: dt, \\] where $\\gamma$ is a real analytic function defined on a neighborhood of the origin in $(t,x)\\in \\R^N\\times \\R^n$, satisfying $\\gamma_0(x)\\equiv x$, $\\psi$ is a cutoff function supported near $0\\in \\R^n$, and $K$ is a \"multi-parameter singular kernel\" supported near $0\\in \\R^N$. A main example is when $K$ is a \"product kernel.\" We also study maximal operators of the form, \\[ \\mathcal{M} f(x) = \\psi(x)\\sup_{0<\\delta_1,..., \\delta_N<<1} \\int_{|t|<1} |f(\\gamma_{\\delta_1 t_1,...,\\delta_N t_N}"},"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":"1105.4589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-23T19:31:25Z","cross_cats_sorted":[],"title_canon_sha256":"eff068085b2c6e5ed21da45082c5436b6b3c329291f42e8e75d0e4b2fa115a1f","abstract_canon_sha256":"2fec343d4379d8332effef963dde9c8a21ea9deb663f89a3e33a0026e5174205"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:23.113130Z","signature_b64":"kINYHGQGZNB8pGgLpB2dyeQAJ2CmdLhStiw6vCV+FJ1BW4FYWHcBrHsB40CyNbn8eZzBxdDl6wC3yKP/kJEWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb740eb84bbf0976206add44fb4e1c870bd96cc81449aa8a491e7dae5f464f33","last_reissued_at":"2026-05-18T04:21:23.112721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:23.112721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-parameter singular Radon transforms III: real analytic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brian Street, Elias M. 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