{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SKFUB7ZT55T2PPK4PQQIQVBSNC","short_pith_number":"pith:SKFUB7ZT","schema_version":"1.0","canonical_sha256":"928b40ff33ef67a7bd5c7c2088543268af978ca10d9917fc25251df2decc3626","source":{"kind":"arxiv","id":"1512.07518","version":2},"attestation_state":"computed","paper":{"title":"$\\ell^p\\big(\\mathbb Z^d\\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bartosz Trojan, Elias M. Stein, Mariusz Mirek","submitted_at":"2015-12-23T15:36:19Z","abstract_excerpt":"We prove $\\ell^p\\big(\\mathbb Z^d\\big)$ bounds, for $p\\in(1, \\infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type, and their applications to pointwise ergodic theory. Our new approach is based on a unified analysis of both types of operators, and also yields an extension to the vector-valued form of these results."},"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":"1512.07518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-23T15:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"ec205b6f392108d49526feae7261446ee320c85cf4cd39921c7f81080bb366f4","abstract_canon_sha256":"3e8ba0b7c699c6eada8cbc2215b919c730063196ae13af8f6cd29ede5353dbee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:03.638574Z","signature_b64":"MdLPyO0Pcqw0kyYpg2f9xF696yiW08e3F7/YoV9NzLBTLfEt4NUx6TQWYA74i68m8VUOMvDGqDPUsA6rbWh2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"928b40ff33ef67a7bd5c7c2088543268af978ca10d9917fc25251df2decc3626","last_reissued_at":"2026-05-18T00:02:03.637915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:03.637915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\ell^p\\big(\\mathbb Z^d\\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bartosz Trojan, Elias M. Stein, Mariusz Mirek","submitted_at":"2015-12-23T15:36:19Z","abstract_excerpt":"We prove $\\ell^p\\big(\\mathbb Z^d\\big)$ bounds, for $p\\in(1, \\infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type, and their applications to pointwise ergodic theory. Our new approach is based on a unified analysis of both types of operators, and also yields an extension to the vector-valued form of these results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07518","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":"1512.07518","created_at":"2026-05-18T00:02:03.638011+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.07518v2","created_at":"2026-05-18T00:02:03.638011+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07518","created_at":"2026-05-18T00:02:03.638011+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKFUB7ZT55T2","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKFUB7ZT55T2PPK4","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKFUB7ZT","created_at":"2026-05-18T12:29:42.218222+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/SKFUB7ZT55T2PPK4PQQIQVBSNC","json":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC.json","graph_json":"https://pith.science/api/pith-number/SKFUB7ZT55T2PPK4PQQIQVBSNC/graph.json","events_json":"https://pith.science/api/pith-number/SKFUB7ZT55T2PPK4PQQIQVBSNC/events.json","paper":"https://pith.science/paper/SKFUB7ZT"},"agent_actions":{"view_html":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC","download_json":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC.json","view_paper":"https://pith.science/paper/SKFUB7ZT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.07518&json=true","fetch_graph":"https://pith.science/api/pith-number/SKFUB7ZT55T2PPK4PQQIQVBSNC/graph.json","fetch_events":"https://pith.science/api/pith-number/SKFUB7ZT55T2PPK4PQQIQVBSNC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/action/storage_attestation","attest_author":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/action/author_attestation","sign_citation":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/action/citation_signature","submit_replication":"https://pith.science/pith/SKFUB7ZT55T2PPK4PQQIQVBSNC/action/replication_record"}},"created_at":"2026-05-18T00:02:03.638011+00:00","updated_at":"2026-05-18T00:02:03.638011+00:00"}