{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:K7TDPS4ROGCWG7SZFTRCGYU4LE","short_pith_number":"pith:K7TDPS4R","schema_version":"1.0","canonical_sha256":"57e637cb917185637e592ce223629c590d7d94356388bec4f42d2a6247b92a5a","source":{"kind":"arxiv","id":"1104.2199","version":3},"attestation_state":"computed","paper":{"title":"An A_p --A_infty inequality for the Hilbert Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael T Lacey","submitted_at":"2011-04-12T12:59:43Z","abstract_excerpt":"Continuing a theme of Lerner and Hytonen-Perez, we establish an L^p(w) inequality for a Haar shift operator of bounded complexity, that quantifies the contribution of the A_infty characteristic of the weight to the L^p norm. Here, 1<p<\\infty. The Hytonen-Perez inequality is only for p=2, and we improve an inequality of the author and 6 other collaborators. As a corollary, the same inequality holds for all Calderon-Zygmund operators in the convex hull of Haar shifts of a bounded complexity, of which the canonical example is the Hilbert transform. We conjecture that the same inequality holds for"},"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":"1104.2199","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-12T12:59:43Z","cross_cats_sorted":[],"title_canon_sha256":"765c4b0b890d3fbb291750692373d545294f5a155ff719087a8ebae46142f647","abstract_canon_sha256":"456e3989207662da442df81636c6af808d80d70dd0acaafc2ce91198e777326e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:31.960646Z","signature_b64":"QIzck6+Hdtjaata4VE2gVREk9FZzAq7lX1WtpC1E1p9BbyRw5wXWYau+RxE9gCZHJ6XaZY5IvZatudDy4lKXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57e637cb917185637e592ce223629c590d7d94356388bec4f42d2a6247b92a5a","last_reissued_at":"2026-05-18T04:19:31.960230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:31.960230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An A_p --A_infty inequality for the Hilbert Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael T Lacey","submitted_at":"2011-04-12T12:59:43Z","abstract_excerpt":"Continuing a theme of Lerner and Hytonen-Perez, we establish an L^p(w) inequality for a Haar shift operator of bounded complexity, that quantifies the contribution of the A_infty characteristic of the weight to the L^p norm. Here, 1<p<\\infty. The Hytonen-Perez inequality is only for p=2, and we improve an inequality of the author and 6 other collaborators. As a corollary, the same inequality holds for all Calderon-Zygmund operators in the convex hull of Haar shifts of a bounded complexity, of which the canonical example is the Hilbert transform. We conjecture that the same inequality holds for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2199","kind":"arxiv","version":3},"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":"1104.2199","created_at":"2026-05-18T04:19:31.960287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.2199v3","created_at":"2026-05-18T04:19:31.960287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2199","created_at":"2026-05-18T04:19:31.960287+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7TDPS4ROGCW","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7TDPS4ROGCWG7SZ","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7TDPS4R","created_at":"2026-05-18T12:26:32.869790+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/K7TDPS4ROGCWG7SZFTRCGYU4LE","json":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE.json","graph_json":"https://pith.science/api/pith-number/K7TDPS4ROGCWG7SZFTRCGYU4LE/graph.json","events_json":"https://pith.science/api/pith-number/K7TDPS4ROGCWG7SZFTRCGYU4LE/events.json","paper":"https://pith.science/paper/K7TDPS4R"},"agent_actions":{"view_html":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE","download_json":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE.json","view_paper":"https://pith.science/paper/K7TDPS4R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.2199&json=true","fetch_graph":"https://pith.science/api/pith-number/K7TDPS4ROGCWG7SZFTRCGYU4LE/graph.json","fetch_events":"https://pith.science/api/pith-number/K7TDPS4ROGCWG7SZFTRCGYU4LE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE/action/storage_attestation","attest_author":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE/action/author_attestation","sign_citation":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE/action/citation_signature","submit_replication":"https://pith.science/pith/K7TDPS4ROGCWG7SZFTRCGYU4LE/action/replication_record"}},"created_at":"2026-05-18T04:19:31.960287+00:00","updated_at":"2026-05-18T04:19:31.960287+00:00"}