{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DE2O4MQLEDJYKJKMZQLZDZ6WJS","short_pith_number":"pith:DE2O4MQL","schema_version":"1.0","canonical_sha256":"1934ee320b20d385254ccc1791e7d64cbb41fb31f1988257addf6ba7db90908f","source":{"kind":"arxiv","id":"1303.6351","version":1},"attestation_state":"computed","paper":{"title":"Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David S. McCormick, James C. Robinson, Jose L. Rodrigo","submitted_at":"2013-03-26T00:07:22Z","abstract_excerpt":"Using elementary arguments based on the Fourier transform we prove that for $1 \\leq q < p < \\infty$ and $s \\geq 0$ with $s > n(1/2-1/p)$, if $f \\in L^{q,\\infty}(\\R^n) \\cap \\dot{H}^s(\\R^n)$ then $f \\in L^p(\\R^n)$ and there exists a constant $c_{p,q,s}$ such that\n  \\[ \\|f\\|_{L^p} \\leq c_{p,q,s} \\|f\\|_{L^{q,\\infty}}^\\theta \\|f\\|_{\\dot H^s}^{1-\\theta}, \\] where $1/p = \\theta/q + (1-\\theta)(1/2-s/n)$. In particular, in $\\R^2$ we obtain the generalised Ladyzhenskaya inequality $\\|f\\|_{L^4}\\le c\\|f\\|_{L^{2,\\infty}}^{1/2}\\|f\\|_{\\dot H^1}^{1/2}$. We also show that for $s=n/2$ the norm in $\\|f\\|_{\\dot H"},"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":"1303.6351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T00:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"0208d29cc188de5c2cbe94b90201243e13d4687313ea89b753c9addad64e752a","abstract_canon_sha256":"738c2e2feeb43f91fb51937e015e431ab6e5b957a33a98dca198312a5542eb80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:49.674496Z","signature_b64":"+/kc7+RTdxcXJ/gHGAtxxMMWOcXPJXf6nqGA66PvZ6pN2I6uvmIeaOm7atcRPu1GqAalihXa6qzhEDyds92DCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1934ee320b20d385254ccc1791e7d64cbb41fb31f1988257addf6ba7db90908f","last_reissued_at":"2026-05-18T03:29:49.673743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:49.673743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David S. McCormick, James C. Robinson, Jose L. Rodrigo","submitted_at":"2013-03-26T00:07:22Z","abstract_excerpt":"Using elementary arguments based on the Fourier transform we prove that for $1 \\leq q < p < \\infty$ and $s \\geq 0$ with $s > n(1/2-1/p)$, if $f \\in L^{q,\\infty}(\\R^n) \\cap \\dot{H}^s(\\R^n)$ then $f \\in L^p(\\R^n)$ and there exists a constant $c_{p,q,s}$ such that\n  \\[ \\|f\\|_{L^p} \\leq c_{p,q,s} \\|f\\|_{L^{q,\\infty}}^\\theta \\|f\\|_{\\dot H^s}^{1-\\theta}, \\] where $1/p = \\theta/q + (1-\\theta)(1/2-s/n)$. In particular, in $\\R^2$ we obtain the generalised Ladyzhenskaya inequality $\\|f\\|_{L^4}\\le c\\|f\\|_{L^{2,\\infty}}^{1/2}\\|f\\|_{\\dot H^1}^{1/2}$. We also show that for $s=n/2$ the norm in $\\|f\\|_{\\dot H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6351","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":"1303.6351","created_at":"2026-05-18T03:29:49.673851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.6351v1","created_at":"2026-05-18T03:29:49.673851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6351","created_at":"2026-05-18T03:29:49.673851+00:00"},{"alias_kind":"pith_short_12","alias_value":"DE2O4MQLEDJY","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DE2O4MQLEDJYKJKM","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DE2O4MQL","created_at":"2026-05-18T12:27:43.054852+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/DE2O4MQLEDJYKJKMZQLZDZ6WJS","json":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS.json","graph_json":"https://pith.science/api/pith-number/DE2O4MQLEDJYKJKMZQLZDZ6WJS/graph.json","events_json":"https://pith.science/api/pith-number/DE2O4MQLEDJYKJKMZQLZDZ6WJS/events.json","paper":"https://pith.science/paper/DE2O4MQL"},"agent_actions":{"view_html":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS","download_json":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS.json","view_paper":"https://pith.science/paper/DE2O4MQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.6351&json=true","fetch_graph":"https://pith.science/api/pith-number/DE2O4MQLEDJYKJKMZQLZDZ6WJS/graph.json","fetch_events":"https://pith.science/api/pith-number/DE2O4MQLEDJYKJKMZQLZDZ6WJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS/action/storage_attestation","attest_author":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS/action/author_attestation","sign_citation":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS/action/citation_signature","submit_replication":"https://pith.science/pith/DE2O4MQLEDJYKJKMZQLZDZ6WJS/action/replication_record"}},"created_at":"2026-05-18T03:29:49.673851+00:00","updated_at":"2026-05-18T03:29:49.673851+00:00"}