{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DOH5WIEPAYBNNZUU4ULVN6EIIP","short_pith_number":"pith:DOH5WIEP","schema_version":"1.0","canonical_sha256":"1b8fdb208f0602d6e694e51756f88843c214097bc90cf70a7b38488dc5fea93b","source":{"kind":"arxiv","id":"1609.07364","version":1},"attestation_state":"computed","paper":{"title":"Interpolation for Hardy Spaces: Marcinkiewicz decomposition, Complex Interpolation and Holomorphic Martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Paul F.X. M\\\"uller, Peter Yuditskii","submitted_at":"2016-09-23T13:52:28Z","abstract_excerpt":"The real and complex interpolation spaces for the classical Hardy spaces $H^1$ and $H^\\infty$ were determined in 1983 by P.W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate approximation problem for the $L^ 1$ metric. Specifically for $ f \\in H^p$ the size of $$ {\\rm{inf}} \\{ \\| f - f_1 \\| _1 \\,:\\, f_1 \\in H^\\infty ,\\, \\|f_1\\|_\\infty \\le \\lambda \\}$$ needs to be determined for any $ \\lambda>0 $. In the present paper we develop a new set of truncation formulae for obtaining the Marcinkiewicz decomposition of $(H^1, H^\\infty) $. We revi"},"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":"1609.07364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-23T13:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"eb63a3a8bf7032b2ada0c2acdc138dddf0fbdad784e089a0e93eda3b86ebf5d6","abstract_canon_sha256":"b93f9171c6d754fe670d2361dd342b95cadb0533534e87c3580eaae905a1df13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:01.508609Z","signature_b64":"ZRRThz2AQK2fiivmu/BV0O/JziuT/kYXgYLj7aXTpXKUcn+RykeYKbnOi/76G60CF1iv4IeoZtbNJRNhQ3ZxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b8fdb208f0602d6e694e51756f88843c214097bc90cf70a7b38488dc5fea93b","last_reissued_at":"2026-05-18T01:04:01.507882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:01.507882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpolation for Hardy Spaces: Marcinkiewicz decomposition, Complex Interpolation and Holomorphic Martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Paul F.X. M\\\"uller, Peter Yuditskii","submitted_at":"2016-09-23T13:52:28Z","abstract_excerpt":"The real and complex interpolation spaces for the classical Hardy spaces $H^1$ and $H^\\infty$ were determined in 1983 by P.W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate approximation problem for the $L^ 1$ metric. Specifically for $ f \\in H^p$ the size of $$ {\\rm{inf}} \\{ \\| f - f_1 \\| _1 \\,:\\, f_1 \\in H^\\infty ,\\, \\|f_1\\|_\\infty \\le \\lambda \\}$$ needs to be determined for any $ \\lambda>0 $. In the present paper we develop a new set of truncation formulae for obtaining the Marcinkiewicz decomposition of $(H^1, H^\\infty) $. We revi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07364","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":"1609.07364","created_at":"2026-05-18T01:04:01.508012+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07364v1","created_at":"2026-05-18T01:04:01.508012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07364","created_at":"2026-05-18T01:04:01.508012+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOH5WIEPAYBN","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOH5WIEPAYBNNZUU","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOH5WIEP","created_at":"2026-05-18T12:30:12.583610+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/DOH5WIEPAYBNNZUU4ULVN6EIIP","json":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP.json","graph_json":"https://pith.science/api/pith-number/DOH5WIEPAYBNNZUU4ULVN6EIIP/graph.json","events_json":"https://pith.science/api/pith-number/DOH5WIEPAYBNNZUU4ULVN6EIIP/events.json","paper":"https://pith.science/paper/DOH5WIEP"},"agent_actions":{"view_html":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP","download_json":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP.json","view_paper":"https://pith.science/paper/DOH5WIEP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07364&json=true","fetch_graph":"https://pith.science/api/pith-number/DOH5WIEPAYBNNZUU4ULVN6EIIP/graph.json","fetch_events":"https://pith.science/api/pith-number/DOH5WIEPAYBNNZUU4ULVN6EIIP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP/action/storage_attestation","attest_author":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP/action/author_attestation","sign_citation":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP/action/citation_signature","submit_replication":"https://pith.science/pith/DOH5WIEPAYBNNZUU4ULVN6EIIP/action/replication_record"}},"created_at":"2026-05-18T01:04:01.508012+00:00","updated_at":"2026-05-18T01:04:01.508012+00:00"}