{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4HR2T7A3NMCYM536BUAKNQ3QVQ","short_pith_number":"pith:4HR2T7A3","schema_version":"1.0","canonical_sha256":"e1e3a9fc1b6b0586777e0d00a6c370ac30d23f6794226ec455da55d3a82f1abc","source":{"kind":"arxiv","id":"1407.7120","version":2},"attestation_state":"computed","paper":{"title":"On the constants of the Bohnenblust-Hille inequality and Hardy--Littlewood inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Gustavo Araujo","submitted_at":"2014-07-26T11:02:21Z","abstract_excerpt":"In this paper, among other results, we improve the best known estimates for the constants of the generalized Bohnenblust-Hille inequality. These enhancements are then used to improve the best known constants of the Hardy--Littlewood inequality; this inequality asserts that for a positive integer $m\\geq2$ with $2m\\leq p\\leq\\infty$ and $\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$ there exists a constant $C_{m,p}^{\\mathbb{K}}\\geq1$ such that, for all continuous $m$--linear forms $T:\\ell_{p}^{n}\\times\\cdots\\times\\ell_{p}^{n}\\rightarrow\\mathbb{K}$, and all positive integers $n$,% \\[ \\left( \\sum_{j_{1},."},"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":"1407.7120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-26T11:02:21Z","cross_cats_sorted":[],"title_canon_sha256":"190459323f49697cdd34735a6800f7ded545aac0b41e7088c584c364a6de13a2","abstract_canon_sha256":"ffd1b969b671c687e51693dcf7d340a5fd99aab5aaf77fd6fb6b90d7a006efe2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:48.280601Z","signature_b64":"4Dp2QEQdgffF+8Sm4GvgEyft1h4eaZ4La23YM3Wy8/spRDehBtrwybXx7bZ/6CZpisMUxlAfUHCxl8EpRkX1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1e3a9fc1b6b0586777e0d00a6c370ac30d23f6794226ec455da55d3a82f1abc","last_reissued_at":"2026-05-18T02:45:48.280108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:48.280108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the constants of the Bohnenblust-Hille inequality and Hardy--Littlewood inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Gustavo Araujo","submitted_at":"2014-07-26T11:02:21Z","abstract_excerpt":"In this paper, among other results, we improve the best known estimates for the constants of the generalized Bohnenblust-Hille inequality. These enhancements are then used to improve the best known constants of the Hardy--Littlewood inequality; this inequality asserts that for a positive integer $m\\geq2$ with $2m\\leq p\\leq\\infty$ and $\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$ there exists a constant $C_{m,p}^{\\mathbb{K}}\\geq1$ such that, for all continuous $m$--linear forms $T:\\ell_{p}^{n}\\times\\cdots\\times\\ell_{p}^{n}\\rightarrow\\mathbb{K}$, and all positive integers $n$,% \\[ \\left( \\sum_{j_{1},."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7120","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":"1407.7120","created_at":"2026-05-18T02:45:48.280167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.7120v2","created_at":"2026-05-18T02:45:48.280167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7120","created_at":"2026-05-18T02:45:48.280167+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HR2T7A3NMCY","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HR2T7A3NMCYM536","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HR2T7A3","created_at":"2026-05-18T12:28:14.216126+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/4HR2T7A3NMCYM536BUAKNQ3QVQ","json":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ.json","graph_json":"https://pith.science/api/pith-number/4HR2T7A3NMCYM536BUAKNQ3QVQ/graph.json","events_json":"https://pith.science/api/pith-number/4HR2T7A3NMCYM536BUAKNQ3QVQ/events.json","paper":"https://pith.science/paper/4HR2T7A3"},"agent_actions":{"view_html":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ","download_json":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ.json","view_paper":"https://pith.science/paper/4HR2T7A3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.7120&json=true","fetch_graph":"https://pith.science/api/pith-number/4HR2T7A3NMCYM536BUAKNQ3QVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4HR2T7A3NMCYM536BUAKNQ3QVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ/action/storage_attestation","attest_author":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ/action/author_attestation","sign_citation":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ/action/citation_signature","submit_replication":"https://pith.science/pith/4HR2T7A3NMCYM536BUAKNQ3QVQ/action/replication_record"}},"created_at":"2026-05-18T02:45:48.280167+00:00","updated_at":"2026-05-18T02:45:48.280167+00:00"}