{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:X7XYL6347VXRYIW3H74LXNE6CS","short_pith_number":"pith:X7XYL634","schema_version":"1.0","canonical_sha256":"bfef85fb7cfd6f1c22db3ff8bbb49e149c317af0a7f45061f3445cc36001f90a","source":{"kind":"arxiv","id":"2501.03050","version":1},"attestation_state":"computed","paper":{"title":"Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_\\infty$ Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Dachun Yang, Fan Bu, Tuomas Hyt\\\"onen, Wen Yuan","submitted_at":"2025-01-06T14:38:23Z","abstract_excerpt":"Introduced by A. Volberg, matrix $A_{p,\\infty}$ weights provide a suitable generalization of Muckenhoupt $A_\\infty$ weights from the classical theory. In our previous work, we established new characterizations of these weights. Here, we use these results to study inhomogeneous Besov-type and Triebel--Lizorkin-type spaces with such weights. In particular, we characterize these spaces, in terms of the $\\varphi$-transform, molecules, and wavelets, and obtain the boundedness of almost diagonal operators, pseudo-differential operators, trace operators, pointwise multipliers, and Calder\\'on--Zygmund"},"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":"2501.03050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-01-06T14:38:23Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"57e30e8d7c336f6ae59d105120f522cccd9e05d8a7c01cb5c925ae6fd621b90f","abstract_canon_sha256":"4155988b405c9cfbb02907ce698ecc5f0ce317237c8fd6f42726e2aeda0eb102"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:29.877737Z","signature_b64":"HV4HV3WAkv3I5uTFUMFrXqUCMunJ1VDB/Gqz9TQZvCbpgXnqeRwRvmBqBVZDkQ9ezfsnTDMNwq64SJLfV+EDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfef85fb7cfd6f1c22db3ff8bbb49e149c317af0a7f45061f3445cc36001f90a","last_reissued_at":"2026-07-05T09:57:29.877312Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:29.877312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_\\infty$ Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Dachun Yang, Fan Bu, Tuomas Hyt\\\"onen, Wen Yuan","submitted_at":"2025-01-06T14:38:23Z","abstract_excerpt":"Introduced by A. Volberg, matrix $A_{p,\\infty}$ weights provide a suitable generalization of Muckenhoupt $A_\\infty$ weights from the classical theory. In our previous work, we established new characterizations of these weights. Here, we use these results to study inhomogeneous Besov-type and Triebel--Lizorkin-type spaces with such weights. In particular, we characterize these spaces, in terms of the $\\varphi$-transform, molecules, and wavelets, and obtain the boundedness of almost diagonal operators, pseudo-differential operators, trace operators, pointwise multipliers, and Calder\\'on--Zygmund"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03050","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.03050/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2501.03050","created_at":"2026-07-05T09:57:29.877375+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.03050v1","created_at":"2026-07-05T09:57:29.877375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03050","created_at":"2026-07-05T09:57:29.877375+00:00"},{"alias_kind":"pith_short_12","alias_value":"X7XYL6347VXR","created_at":"2026-07-05T09:57:29.877375+00:00"},{"alias_kind":"pith_short_16","alias_value":"X7XYL6347VXRYIW3","created_at":"2026-07-05T09:57:29.877375+00:00"},{"alias_kind":"pith_short_8","alias_value":"X7XYL634","created_at":"2026-07-05T09:57:29.877375+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.19135","citing_title":"Weighted Bourgain-Morrey-Besov type and Triebel-Lizorkin type spaces associated with operators","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS","json":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS.json","graph_json":"https://pith.science/api/pith-number/X7XYL6347VXRYIW3H74LXNE6CS/graph.json","events_json":"https://pith.science/api/pith-number/X7XYL6347VXRYIW3H74LXNE6CS/events.json","paper":"https://pith.science/paper/X7XYL634"},"agent_actions":{"view_html":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS","download_json":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS.json","view_paper":"https://pith.science/paper/X7XYL634","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.03050&json=true","fetch_graph":"https://pith.science/api/pith-number/X7XYL6347VXRYIW3H74LXNE6CS/graph.json","fetch_events":"https://pith.science/api/pith-number/X7XYL6347VXRYIW3H74LXNE6CS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS/action/storage_attestation","attest_author":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS/action/author_attestation","sign_citation":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS/action/citation_signature","submit_replication":"https://pith.science/pith/X7XYL6347VXRYIW3H74LXNE6CS/action/replication_record"}},"created_at":"2026-07-05T09:57:29.877375+00:00","updated_at":"2026-07-05T09:57:29.877375+00:00"}