{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SRKNA25RZULGWAUWF2LJJN4MUD","short_pith_number":"pith:SRKNA25R","schema_version":"1.0","canonical_sha256":"9454d06bb1cd166b02962e9694b78ca0d380a3fe4d8f7f00f01f844388cae88e","source":{"kind":"arxiv","id":"1602.00549","version":1},"attestation_state":"computed","paper":{"title":"Weighted $L^p$ bounds for the Marcinkiewicz integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guoen Hu, Meng Qu","submitted_at":"2016-02-01T14:49:53Z","abstract_excerpt":"Let $\\Omega$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and $\\mathcal{M}_{\\Omega}$ be the higher-dimensional Marcinkiewicz integral associated with $\\Omega$. In this paper, the authors proved that if $\\Omega\\in L^q(S^{n-1})$ for some $q\\in (1,\\,\\infty]$, then for $p\\in (q',\\,\\infty)$ and $w\\in A_{p}(\\mathbb{R}^n)$, the bound of $\\mathcal{M}_{\\Omega}$ on $L^p(\\mathbb{R}^n,\\,w)$ is less than $C[w]_{A_{p/q'}}^{2\\max\\{1,\\,\\frac{1}{p-q'}\\}}$."},"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":"1602.00549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-01T14:49:53Z","cross_cats_sorted":[],"title_canon_sha256":"d362b4b1b21fb9059c78d03a3e07ab9bad5ab914f0fe4624811723c8288a07f1","abstract_canon_sha256":"a6028fa474a5d63cb0b60246338d32f8244e609ddce1ae92e838b73bde121e52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:35.124954Z","signature_b64":"ILWhn4tegyOI+PnNdoWpWleJtjNd9ObC6AQRGYnqcjuzCmVXOO9VUIbC3OdLO7f6xqbUhuqw50OCc2LHVu4KAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9454d06bb1cd166b02962e9694b78ca0d380a3fe4d8f7f00f01f844388cae88e","last_reissued_at":"2026-05-18T01:21:35.124385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:35.124385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted $L^p$ bounds for the Marcinkiewicz integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guoen Hu, Meng Qu","submitted_at":"2016-02-01T14:49:53Z","abstract_excerpt":"Let $\\Omega$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and $\\mathcal{M}_{\\Omega}$ be the higher-dimensional Marcinkiewicz integral associated with $\\Omega$. In this paper, the authors proved that if $\\Omega\\in L^q(S^{n-1})$ for some $q\\in (1,\\,\\infty]$, then for $p\\in (q',\\,\\infty)$ and $w\\in A_{p}(\\mathbb{R}^n)$, the bound of $\\mathcal{M}_{\\Omega}$ on $L^p(\\mathbb{R}^n,\\,w)$ is less than $C[w]_{A_{p/q'}}^{2\\max\\{1,\\,\\frac{1}{p-q'}\\}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00549","kind":"arxiv","version":1},"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":"1602.00549","created_at":"2026-05-18T01:21:35.124495+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.00549v1","created_at":"2026-05-18T01:21:35.124495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00549","created_at":"2026-05-18T01:21:35.124495+00:00"},{"alias_kind":"pith_short_12","alias_value":"SRKNA25RZULG","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SRKNA25RZULGWAUW","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SRKNA25R","created_at":"2026-05-18T12:30:44.179134+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/SRKNA25RZULGWAUWF2LJJN4MUD","json":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD.json","graph_json":"https://pith.science/api/pith-number/SRKNA25RZULGWAUWF2LJJN4MUD/graph.json","events_json":"https://pith.science/api/pith-number/SRKNA25RZULGWAUWF2LJJN4MUD/events.json","paper":"https://pith.science/paper/SRKNA25R"},"agent_actions":{"view_html":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD","download_json":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD.json","view_paper":"https://pith.science/paper/SRKNA25R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.00549&json=true","fetch_graph":"https://pith.science/api/pith-number/SRKNA25RZULGWAUWF2LJJN4MUD/graph.json","fetch_events":"https://pith.science/api/pith-number/SRKNA25RZULGWAUWF2LJJN4MUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD/action/storage_attestation","attest_author":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD/action/author_attestation","sign_citation":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD/action/citation_signature","submit_replication":"https://pith.science/pith/SRKNA25RZULGWAUWF2LJJN4MUD/action/replication_record"}},"created_at":"2026-05-18T01:21:35.124495+00:00","updated_at":"2026-05-18T01:21:35.124495+00:00"}