{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VVLDXVCY5TT4WKRHPGCBFFHJWD","short_pith_number":"pith:VVLDXVCY","schema_version":"1.0","canonical_sha256":"ad563bd458ece7cb2a2779841294e9b0cb506dbf3cee61eb5e651463725c2f77","source":{"kind":"arxiv","id":"1112.1744","version":2},"attestation_state":"computed","paper":{"title":"Weighted bounds for variational Walsh-Fourier series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael T. Lacey, Yen Do","submitted_at":"2011-12-08T01:16:37Z","abstract_excerpt":"For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the\n  Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r is a function of w is necessary.) This strengthens a result of Hunt-Young and is a weighted extension of a variation norm Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses phase plane analysis and a weighted extension of a variational inequality of Lepingle."},"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":"1112.1744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-08T01:16:37Z","cross_cats_sorted":[],"title_canon_sha256":"cec4c40ab544c161d3d147619a2cee66f1064716de29ae9dcebab617d854ab6d","abstract_canon_sha256":"ffbaaf4ff1c3e659509daa5b2e485ad7cf9ddf0cf18a2442ab14ddf43dd67562"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:26.870247Z","signature_b64":"KcMxZXOO4NHH/8rGVjXVgNYENotrsiECTi2dtjMAof27MoHBeImfIMTbpj5RWixFfP6zoswH+7aJlVMYVhfKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad563bd458ece7cb2a2779841294e9b0cb506dbf3cee61eb5e651463725c2f77","last_reissued_at":"2026-05-18T04:02:26.869785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:26.869785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted bounds for variational Walsh-Fourier series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael T. Lacey, Yen Do","submitted_at":"2011-12-08T01:16:37Z","abstract_excerpt":"For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the\n  Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r is a function of w is necessary.) This strengthens a result of Hunt-Young and is a weighted extension of a variation norm Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses phase plane analysis and a weighted extension of a variational inequality of Lepingle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1744","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":"1112.1744","created_at":"2026-05-18T04:02:26.869849+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1744v2","created_at":"2026-05-18T04:02:26.869849+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1744","created_at":"2026-05-18T04:02:26.869849+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVLDXVCY5TT4","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVLDXVCY5TT4WKRH","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVLDXVCY","created_at":"2026-05-18T12:26:44.992195+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/VVLDXVCY5TT4WKRHPGCBFFHJWD","json":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD.json","graph_json":"https://pith.science/api/pith-number/VVLDXVCY5TT4WKRHPGCBFFHJWD/graph.json","events_json":"https://pith.science/api/pith-number/VVLDXVCY5TT4WKRHPGCBFFHJWD/events.json","paper":"https://pith.science/paper/VVLDXVCY"},"agent_actions":{"view_html":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD","download_json":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD.json","view_paper":"https://pith.science/paper/VVLDXVCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1744&json=true","fetch_graph":"https://pith.science/api/pith-number/VVLDXVCY5TT4WKRHPGCBFFHJWD/graph.json","fetch_events":"https://pith.science/api/pith-number/VVLDXVCY5TT4WKRHPGCBFFHJWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD/action/storage_attestation","attest_author":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD/action/author_attestation","sign_citation":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD/action/citation_signature","submit_replication":"https://pith.science/pith/VVLDXVCY5TT4WKRHPGCBFFHJWD/action/replication_record"}},"created_at":"2026-05-18T04:02:26.869849+00:00","updated_at":"2026-05-18T04:02:26.869849+00:00"}