{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z7BFJMAWHYZSHG7D4Y64KTXNF4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1f9733139feba108ecffe2e8b70670194dcd177c77e1bba53865dd34099799c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-23T19:32:16Z","title_canon_sha256":"7f43d914491e22255708e2dcba37a31060b0a3af79881fb49ac1092968e0b582"},"schema_version":"1.0","source":{"id":"1105.4590","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4590","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4590v2","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4590","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"Z7BFJMAWHYZS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z7BFJMAWHYZSHG7D","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z7BFJMAW","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:1c6949552e0061e75c04481627a71a878a44e8a3fc2b644263fba741a1ca116d","target":"graph","created_at":"2026-05-18T03:17:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The purpose of this paper is to study the $L^p$ boundedness of operators of the form \\[ f\\mapsto \\psi(x) \\int f(\\gamma_t(x))K(t)\\: dt, \\] where $\\gamma_t(x)$ is a $C^\\infty$ 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 $C^\\infty$ cutoff function supported on a small neighborhood of $0\\in \\R^n$, and $K$ is a \"multi-parameter singular kernel\" supported on a small neighborhood of $0\\in \\R^N$. We also study associated maximal operators. The goal is, given an appropriate class of kernels $K$, to give conditions on $\\ga","authors_text":"Brian Street, Elias M. Stein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-23T19:32:16Z","title":"Multi-parameter singular Radon transforms II: the L^p theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4590","kind":"arxiv","version":2},"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:ccaed8f2d76c5cc7d2534d0d059d9adcb552e8a4589304241426e4a8773f42d6","target":"record","created_at":"2026-05-18T03:17:12Z","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":"1f9733139feba108ecffe2e8b70670194dcd177c77e1bba53865dd34099799c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-23T19:32:16Z","title_canon_sha256":"7f43d914491e22255708e2dcba37a31060b0a3af79881fb49ac1092968e0b582"},"schema_version":"1.0","source":{"id":"1105.4590","kind":"arxiv","version":2}},"canonical_sha256":"cfc254b0163e33239be3e63dc54eed2f3843efb58bb10e93ffd9edf72ba673b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfc254b0163e33239be3e63dc54eed2f3843efb58bb10e93ffd9edf72ba673b8","first_computed_at":"2026-05-18T03:17:12.230833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:12.230833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8bVfCP6oX6E6tbz3yes3fAuymatqD6nKKNJXIyF/yl1hQqwwf2GKVOiXLs90AgmbOplcZQs89eNdR5l8vS70CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:12.231701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4590","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccaed8f2d76c5cc7d2534d0d059d9adcb552e8a4589304241426e4a8773f42d6","sha256:1c6949552e0061e75c04481627a71a878a44e8a3fc2b644263fba741a1ca116d"],"state_sha256":"e86b497ad59afde25820f2d82ee5b095a4273d91539e96b8e7f854727e7239be"}