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We prove that for $p>2.18006$ the optimal constants $C_{(m),p}$ are $\\left( 2^{\\frac{1}{2}-\\frac{1}{p}}\\right) ^{m-1}.$ When $p=\\in"},"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":"1604.06323","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-21T14:30:51Z","cross_cats_sorted":[],"title_canon_sha256":"fae44af7a84bd3338ce57b519feccdc3d596426158a6bc6c0b43a985fb888f4c","abstract_canon_sha256":"2a2e3532954b940362dc18796efc2d8911d11e98ded9c2394bae7192f62a82c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:59.102052Z","signature_b64":"/iiAnkhbm3q3iQvLC+ENoWB+3WslEInQl9EoD/k57X3Han4utbmk2beE7x9/Kn83Cx7iGTdJp7A7ZU7pGqRFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66883d1a4102294d62affbe5d770f40b475f650f35b5184d68c00d70f9bb816c","last_reissued_at":"2026-05-18T01:10:59.101487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:59.101487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal constants for a mixed Littlewood type inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel N\\'u\\~nez-Alarc\\'on, Daniel Pellegrino, Tony Nogueira","submitted_at":"2016-04-21T14:30:51Z","abstract_excerpt":"For $p\\in\\lbrack2,\\infty]$ a mixed Littlewood-type inequality asserts that there is a constant $C_{(m),p}\\geq1$ such that \\[ \\left( \\sum_{i_{1}=1}^{\\infty}\\left( \\sum_{i_{2},...,i_{m}=1}^{\\infty }|T(e_{i_{1}},...,e_{i_{m}})|^{2}\\right) ^{\\frac{1}{2}\\frac{p}{p-1}}\\right) ^{\\frac{p-1}{p}}\\leq C_{(m),p}\\Vert T\\Vert \\] for all continuous real-valued $m$-linear forms on $\\ell_{p}\\times c_{0} \\times\\dots\\times c_{0}$ (when $p=\\infty$, $\\ell_{p}$ is replaced by $c_{0})$. We prove that for $p>2.18006$ the optimal constants $C_{(m),p}$ are $\\left( 2^{\\frac{1}{2}-\\frac{1}{p}}\\right) ^{m-1}.$ When $p=\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06323","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":"1604.06323","created_at":"2026-05-18T01:10:59.101584+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06323v2","created_at":"2026-05-18T01:10:59.101584+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06323","created_at":"2026-05-18T01:10:59.101584+00:00"},{"alias_kind":"pith_short_12","alias_value":"M2ED2GSBAIUU","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"M2ED2GSBAIUU2YVP","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"M2ED2GSB","created_at":"2026-05-18T12:30:29.479603+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/M2ED2GSBAIUU2YVP7PS5O4HUBN","json":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN.json","graph_json":"https://pith.science/api/pith-number/M2ED2GSBAIUU2YVP7PS5O4HUBN/graph.json","events_json":"https://pith.science/api/pith-number/M2ED2GSBAIUU2YVP7PS5O4HUBN/events.json","paper":"https://pith.science/paper/M2ED2GSB"},"agent_actions":{"view_html":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN","download_json":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN.json","view_paper":"https://pith.science/paper/M2ED2GSB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06323&json=true","fetch_graph":"https://pith.science/api/pith-number/M2ED2GSBAIUU2YVP7PS5O4HUBN/graph.json","fetch_events":"https://pith.science/api/pith-number/M2ED2GSBAIUU2YVP7PS5O4HUBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN/action/storage_attestation","attest_author":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN/action/author_attestation","sign_citation":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN/action/citation_signature","submit_replication":"https://pith.science/pith/M2ED2GSBAIUU2YVP7PS5O4HUBN/action/replication_record"}},"created_at":"2026-05-18T01:10:59.101584+00:00","updated_at":"2026-05-18T01:10:59.101584+00:00"}