{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DCG3HLVYDUBU7IIP4HNNMESNH2","short_pith_number":"pith:DCG3HLVY","schema_version":"1.0","canonical_sha256":"188db3aeb81d034fa10fe1dad6124d3ea7f53d666589c5be0209c81baf27af54","source":{"kind":"arxiv","id":"1902.08778","version":1},"attestation_state":"computed","paper":{"title":"Three examples of Sharp Commutator Estimates via Harmonic Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Schikorra","submitted_at":"2019-02-23T11:37:13Z","abstract_excerpt":"Recently, Lenzmann and the author observed how to obtain a large class of sharp commutator estimates by a combination of an integration by parts, an harmonic extension, and trace space estimates. In this survey we review this approach in three concrete examples: the Jacobian estimate by Coifman-Lions-Meyer-Semmes, the Coifman-Rochberg-Weiss commutator estimate for Riesz transforms, and a Kato-Ponce-Vega-type inequality."},"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":"1902.08778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-23T11:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"5922bee1efd7a8b9dfbcc24ca2e9eeb5665daf73caa6a9e1c8ef58f71981d224","abstract_canon_sha256":"0b3892df26363f793cf2ca54673ae1b1f5c393da1b8cbceb23806e559f01fdfc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:49.968513Z","signature_b64":"Xus16nMlY05xYlQauRHOfIjHCQMx0sYKw9p6qY9SbbmekriV84/qPSKjQ3g5yL7Whe8hYn0LpVI4QAgYwtsTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"188db3aeb81d034fa10fe1dad6124d3ea7f53d666589c5be0209c81baf27af54","last_reissued_at":"2026-05-17T23:52:49.967782Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:49.967782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three examples of Sharp Commutator Estimates via Harmonic Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Schikorra","submitted_at":"2019-02-23T11:37:13Z","abstract_excerpt":"Recently, Lenzmann and the author observed how to obtain a large class of sharp commutator estimates by a combination of an integration by parts, an harmonic extension, and trace space estimates. In this survey we review this approach in three concrete examples: the Jacobian estimate by Coifman-Lions-Meyer-Semmes, the Coifman-Rochberg-Weiss commutator estimate for Riesz transforms, and a Kato-Ponce-Vega-type inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08778","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":"1902.08778","created_at":"2026-05-17T23:52:49.967893+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.08778v1","created_at":"2026-05-17T23:52:49.967893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08778","created_at":"2026-05-17T23:52:49.967893+00:00"},{"alias_kind":"pith_short_12","alias_value":"DCG3HLVYDUBU","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"DCG3HLVYDUBU7IIP","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"DCG3HLVY","created_at":"2026-05-18T12:33:15.570797+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/DCG3HLVYDUBU7IIP4HNNMESNH2","json":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2.json","graph_json":"https://pith.science/api/pith-number/DCG3HLVYDUBU7IIP4HNNMESNH2/graph.json","events_json":"https://pith.science/api/pith-number/DCG3HLVYDUBU7IIP4HNNMESNH2/events.json","paper":"https://pith.science/paper/DCG3HLVY"},"agent_actions":{"view_html":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2","download_json":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2.json","view_paper":"https://pith.science/paper/DCG3HLVY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.08778&json=true","fetch_graph":"https://pith.science/api/pith-number/DCG3HLVYDUBU7IIP4HNNMESNH2/graph.json","fetch_events":"https://pith.science/api/pith-number/DCG3HLVYDUBU7IIP4HNNMESNH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2/action/storage_attestation","attest_author":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2/action/author_attestation","sign_citation":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2/action/citation_signature","submit_replication":"https://pith.science/pith/DCG3HLVYDUBU7IIP4HNNMESNH2/action/replication_record"}},"created_at":"2026-05-17T23:52:49.967893+00:00","updated_at":"2026-05-17T23:52:49.967893+00:00"}