{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PQXX3E4JA5DMQEUBPVQO3J5X26","short_pith_number":"pith:PQXX3E4J","schema_version":"1.0","canonical_sha256":"7c2f7d93890746c812817d60eda7b7d7b3e49b8a0e56910430f39f38d0afcb29","source":{"kind":"arxiv","id":"1503.01961","version":1},"attestation_state":"computed","paper":{"title":"Projection operators on matrix weighted $L^p$ and a simple sufficient Muckenhoupt condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Morten Grud Rasmussen, Morten Nielsen","submitted_at":"2015-03-06T14:04:33Z","abstract_excerpt":"Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient conditions, which are straightforward to verify, are obtained that ensure that a given matrix weight is contained in the Muckenhoupt matrix $A_p$ class. Applications to singular integral operators with product kernels are considered."},"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":"1503.01961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-06T14:04:33Z","cross_cats_sorted":[],"title_canon_sha256":"ed91c9d2d32326b0bbb3ee496f880eca83199cd35ee1a5905f59764baba9e173","abstract_canon_sha256":"2061becd220cf1d165c6e095445644c4dbdb85bb7112fcd0a5f147ce1e79ef45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:27.168423Z","signature_b64":"9+DJtsz3WysVsYH7OVRyAJuDK/9ev4kDjk0xiBkHh5ecS940uxeytXGn/5iZQmB+p6gEtZXY9n2k1AkBNgspBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c2f7d93890746c812817d60eda7b7d7b3e49b8a0e56910430f39f38d0afcb29","last_reissued_at":"2026-05-18T02:25:27.167850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:27.167850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projection operators on matrix weighted $L^p$ and a simple sufficient Muckenhoupt condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Morten Grud Rasmussen, Morten Nielsen","submitted_at":"2015-03-06T14:04:33Z","abstract_excerpt":"Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient conditions, which are straightforward to verify, are obtained that ensure that a given matrix weight is contained in the Muckenhoupt matrix $A_p$ class. Applications to singular integral operators with product kernels are considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01961","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":"1503.01961","created_at":"2026-05-18T02:25:27.167924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01961v1","created_at":"2026-05-18T02:25:27.167924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01961","created_at":"2026-05-18T02:25:27.167924+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQXX3E4JA5DM","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQXX3E4JA5DMQEUB","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQXX3E4J","created_at":"2026-05-18T12:29:37.295048+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/PQXX3E4JA5DMQEUBPVQO3J5X26","json":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26.json","graph_json":"https://pith.science/api/pith-number/PQXX3E4JA5DMQEUBPVQO3J5X26/graph.json","events_json":"https://pith.science/api/pith-number/PQXX3E4JA5DMQEUBPVQO3J5X26/events.json","paper":"https://pith.science/paper/PQXX3E4J"},"agent_actions":{"view_html":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26","download_json":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26.json","view_paper":"https://pith.science/paper/PQXX3E4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01961&json=true","fetch_graph":"https://pith.science/api/pith-number/PQXX3E4JA5DMQEUBPVQO3J5X26/graph.json","fetch_events":"https://pith.science/api/pith-number/PQXX3E4JA5DMQEUBPVQO3J5X26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26/action/storage_attestation","attest_author":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26/action/author_attestation","sign_citation":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26/action/citation_signature","submit_replication":"https://pith.science/pith/PQXX3E4JA5DMQEUBPVQO3J5X26/action/replication_record"}},"created_at":"2026-05-18T02:25:27.167924+00:00","updated_at":"2026-05-18T02:25:27.167924+00:00"}