{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NI37NNOVUQU6FUZASNXMP2JJIV","short_pith_number":"pith:NI37NNOV","schema_version":"1.0","canonical_sha256":"6a37f6b5d5a429e2d320936ec7e929456334079f90016cf430fb28d0d798ae03","source":{"kind":"arxiv","id":"1508.02355","version":3},"attestation_state":"computed","paper":{"title":"The optimal constants for the real Hardy--Littlewood inequality for bilinear forms on $c_{0}\\times\\ell_{p}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Daniel Nunez-Alarcon, Daniel Pellegrino","submitted_at":"2015-08-10T19:05:00Z","abstract_excerpt":"For $p,q\\geq2$, the Hardy and Littlewood inequalities for real bilinear forms, in its unified formulation, assert that there is a constant $C_{p,q}\\geq1$ such that \\begin{equation} \\left(\\sum\\limits_{j=1}^{\\infty}\\left(\\sum\\limits_{k=1}^{\\infty}\\left\\vert A(e_{j},e_{k})\\right\\vert ^{2}\\right) ^{\\frac{\\lambda}{2}}\\right) ^{\\frac {1}{\\lambda}}\\leq C_{p,q}\\left\\Vert A\\right\\Vert, \\end{equation} with sharp exponent $\\lambda=\\frac{pq}{pq-p-q},$ for all continuous bilinear forms $A:\\ell_{p}\\times\\ell_{q}\\rightarrow\\mathbb{R}$ (as usual, $c_{0}$ replaces $\\ell_{p}$ or $\\ell_{q}$ when $p=\\infty$ or $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":"1508.02355","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-10T19:05:00Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"fc1a370f2d55f1462be29f495dd8689f3911cb9e49cd7b311a0e254c3891934a","abstract_canon_sha256":"255e69da43f556fecda582d35a67d2e0e8867bdd84a2a78ad92e9cd9eb59703d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:42.990841Z","signature_b64":"THELD3oSWWy/x7BWW8tb0SxQr3Nxq2IXj+msRqM5V7eOkSAlYSl18ZK2WCN46A/+qERVOx8IWU+u+kXXwNoTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a37f6b5d5a429e2d320936ec7e929456334079f90016cf430fb28d0d798ae03","last_reissued_at":"2026-05-18T00:19:42.990192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:42.990192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The optimal constants for the real Hardy--Littlewood inequality for bilinear forms on $c_{0}\\times\\ell_{p}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Daniel Nunez-Alarcon, Daniel Pellegrino","submitted_at":"2015-08-10T19:05:00Z","abstract_excerpt":"For $p,q\\geq2$, the Hardy and Littlewood inequalities for real bilinear forms, in its unified formulation, assert that there is a constant $C_{p,q}\\geq1$ such that \\begin{equation} \\left(\\sum\\limits_{j=1}^{\\infty}\\left(\\sum\\limits_{k=1}^{\\infty}\\left\\vert A(e_{j},e_{k})\\right\\vert ^{2}\\right) ^{\\frac{\\lambda}{2}}\\right) ^{\\frac {1}{\\lambda}}\\leq C_{p,q}\\left\\Vert A\\right\\Vert, \\end{equation} with sharp exponent $\\lambda=\\frac{pq}{pq-p-q},$ for all continuous bilinear forms $A:\\ell_{p}\\times\\ell_{q}\\rightarrow\\mathbb{R}$ (as usual, $c_{0}$ replaces $\\ell_{p}$ or $\\ell_{q}$ when $p=\\infty$ or $q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02355","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":"1508.02355","created_at":"2026-05-18T00:19:42.990299+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.02355v3","created_at":"2026-05-18T00:19:42.990299+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02355","created_at":"2026-05-18T00:19:42.990299+00:00"},{"alias_kind":"pith_short_12","alias_value":"NI37NNOVUQU6","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"NI37NNOVUQU6FUZA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"NI37NNOV","created_at":"2026-05-18T12:29:32.376354+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/NI37NNOVUQU6FUZASNXMP2JJIV","json":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV.json","graph_json":"https://pith.science/api/pith-number/NI37NNOVUQU6FUZASNXMP2JJIV/graph.json","events_json":"https://pith.science/api/pith-number/NI37NNOVUQU6FUZASNXMP2JJIV/events.json","paper":"https://pith.science/paper/NI37NNOV"},"agent_actions":{"view_html":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV","download_json":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV.json","view_paper":"https://pith.science/paper/NI37NNOV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.02355&json=true","fetch_graph":"https://pith.science/api/pith-number/NI37NNOVUQU6FUZASNXMP2JJIV/graph.json","fetch_events":"https://pith.science/api/pith-number/NI37NNOVUQU6FUZASNXMP2JJIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV/action/storage_attestation","attest_author":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV/action/author_attestation","sign_citation":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV/action/citation_signature","submit_replication":"https://pith.science/pith/NI37NNOVUQU6FUZASNXMP2JJIV/action/replication_record"}},"created_at":"2026-05-18T00:19:42.990299+00:00","updated_at":"2026-05-18T00:19:42.990299+00:00"}