{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:FFBLVESRLB5QGE62HEEXFAEXIB","short_pith_number":"pith:FFBLVESR","schema_version":"1.0","canonical_sha256":"2942ba9251587b0313da39097280974065ca9f9f1593e5acb870efce9330a719","source":{"kind":"arxiv","id":"1008.0043","version":2},"attestation_state":"computed","paper":{"title":"Equivalent Characterizations for Boundedness of Maximal Singular Integrals on $ax+b$\\,--Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Liguang Liu, Maria Vallarino","submitted_at":"2010-07-31T02:17:01Z","abstract_excerpt":"Let $(S, d, \\rho)$ be the affine group $\\mathrm{R}^n \\ltimes \\mathrm{R}^+$ endowed with the left-invariant Riemannian metric $d$ and the right Haar measure $\\rho$, which is of exponential growth at infinity. In this paper, for any linear operator $T$ on $(S, d, \\rho)$ associated with a kernel $K$ satisfying certain integral size condition and H\\\"ormander's condition, the authors prove that the following four statements regarding the corresponding maximal singular integral $T^\\ast$ are equivalent: $T^\\ast$ is bounded from $L_c^\\infty$ to $\\mathrm{BMO}$, $T^\\ast$ is bounded on $L^p$ for all $p\\i"},"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":"1008.0043","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-31T02:17:01Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c9c0077cee60161d16d881ddf23d772a041a4171fccb34bfd54de30fcf0dc704","abstract_canon_sha256":"e3d037df013e03d179934a8b32ee98c94cc7786fc90cca9b453c1110502fae9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:03.283727Z","signature_b64":"TrWHs+0sDZ3rDRZKp/QsoXyWVpgbqFMQCOntqT1qESPb7XiWg5qz1bOd4MlKBDiPfkPa7b9zLTkp8QWJij65Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2942ba9251587b0313da39097280974065ca9f9f1593e5acb870efce9330a719","last_reissued_at":"2026-05-18T04:17:03.283322Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:03.283322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalent Characterizations for Boundedness of Maximal Singular Integrals on $ax+b$\\,--Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Liguang Liu, Maria Vallarino","submitted_at":"2010-07-31T02:17:01Z","abstract_excerpt":"Let $(S, d, \\rho)$ be the affine group $\\mathrm{R}^n \\ltimes \\mathrm{R}^+$ endowed with the left-invariant Riemannian metric $d$ and the right Haar measure $\\rho$, which is of exponential growth at infinity. In this paper, for any linear operator $T$ on $(S, d, \\rho)$ associated with a kernel $K$ satisfying certain integral size condition and H\\\"ormander's condition, the authors prove that the following four statements regarding the corresponding maximal singular integral $T^\\ast$ are equivalent: $T^\\ast$ is bounded from $L_c^\\infty$ to $\\mathrm{BMO}$, $T^\\ast$ is bounded on $L^p$ for all $p\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0043","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1008.0043","created_at":"2026-05-18T04:17:03.283378+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.0043v2","created_at":"2026-05-18T04:17:03.283378+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0043","created_at":"2026-05-18T04:17:03.283378+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFBLVESRLB5Q","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFBLVESRLB5QGE62","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFBLVESR","created_at":"2026-05-18T12:26:07.630475+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/FFBLVESRLB5QGE62HEEXFAEXIB","json":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB.json","graph_json":"https://pith.science/api/pith-number/FFBLVESRLB5QGE62HEEXFAEXIB/graph.json","events_json":"https://pith.science/api/pith-number/FFBLVESRLB5QGE62HEEXFAEXIB/events.json","paper":"https://pith.science/paper/FFBLVESR"},"agent_actions":{"view_html":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB","download_json":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB.json","view_paper":"https://pith.science/paper/FFBLVESR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.0043&json=true","fetch_graph":"https://pith.science/api/pith-number/FFBLVESRLB5QGE62HEEXFAEXIB/graph.json","fetch_events":"https://pith.science/api/pith-number/FFBLVESRLB5QGE62HEEXFAEXIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB/action/storage_attestation","attest_author":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB/action/author_attestation","sign_citation":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB/action/citation_signature","submit_replication":"https://pith.science/pith/FFBLVESRLB5QGE62HEEXFAEXIB/action/replication_record"}},"created_at":"2026-05-18T04:17:03.283378+00:00","updated_at":"2026-05-18T04:17:03.283378+00:00"}