{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TGG7RFUPJJRKFJTF3CCWS4EI4J","short_pith_number":"pith:TGG7RFUP","schema_version":"1.0","canonical_sha256":"998df8968f4a62a2a665d885697088e24ea712d8405c7b3fc8cec583f662f38e","source":{"kind":"arxiv","id":"1201.4062","version":4},"attestation_state":"computed","paper":{"title":"New Real-Variable Characterizations of Musielak-Orlicz Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Jizheng Huang, Yiyu Liang","submitted_at":"2012-01-19T14:06:45Z","abstract_excerpt":"Let $\\varphi: {\\mathbb R^n}\\times [0,\\infty)\\to[0,\\infty)$ be such that $\\varphi(x,\\cdot)$ is an Orlicz function and $\\varphi(\\cdot,t)$ is a Muckenhoupt $A_\\infty({\\mathbb R^n})$ weight. The Musielak-Orlicz Hardy space $H^{\\varphi}(\\mathbb R^n)$ is defined to be the space of all $f\\in{\\mathcal S}'({\\mathbb R^n})$ such that the grand maximal function $f^*$ belongs to the Musielak-Orlicz space $L^\\varphi(\\mathbb R^n)$. Luong Dang Ky established its atomic characterization. In this paper, the authors establish some new real-variable characterizations of $H^{\\varphi}(\\mathbb R^n)$ in terms of the "},"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":"1201.4062","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-19T14:06:45Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1c348c7d1e25743a3fcc39f9fbf24e8b0c36defdd829d8b9798cb8dca783bd03","abstract_canon_sha256":"31852fabf86011203ff2b425668647694f5484e3a3f73b3f5b1b82bb5fb5be3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:01.529777Z","signature_b64":"67bFh03u5jaHl68M0lGQtFgw+NSJXv9Y8/u01EKsP5sZ0+obALjEM2asX1YPV/KJluBph9z2tBVtwTQI8mNRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"998df8968f4a62a2a665d885697088e24ea712d8405c7b3fc8cec583f662f38e","last_reissued_at":"2026-05-18T03:55:01.529265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:01.529265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Real-Variable Characterizations of Musielak-Orlicz Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Jizheng Huang, Yiyu Liang","submitted_at":"2012-01-19T14:06:45Z","abstract_excerpt":"Let $\\varphi: {\\mathbb R^n}\\times [0,\\infty)\\to[0,\\infty)$ be such that $\\varphi(x,\\cdot)$ is an Orlicz function and $\\varphi(\\cdot,t)$ is a Muckenhoupt $A_\\infty({\\mathbb R^n})$ weight. The Musielak-Orlicz Hardy space $H^{\\varphi}(\\mathbb R^n)$ is defined to be the space of all $f\\in{\\mathcal S}'({\\mathbb R^n})$ such that the grand maximal function $f^*$ belongs to the Musielak-Orlicz space $L^\\varphi(\\mathbb R^n)$. Luong Dang Ky established its atomic characterization. In this paper, the authors establish some new real-variable characterizations of $H^{\\varphi}(\\mathbb R^n)$ in terms of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4062","kind":"arxiv","version":4},"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":"1201.4062","created_at":"2026-05-18T03:55:01.529349+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.4062v4","created_at":"2026-05-18T03:55:01.529349+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4062","created_at":"2026-05-18T03:55:01.529349+00:00"},{"alias_kind":"pith_short_12","alias_value":"TGG7RFUPJJRK","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TGG7RFUPJJRKFJTF","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TGG7RFUP","created_at":"2026-05-18T12:27:23.164592+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/TGG7RFUPJJRKFJTF3CCWS4EI4J","json":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J.json","graph_json":"https://pith.science/api/pith-number/TGG7RFUPJJRKFJTF3CCWS4EI4J/graph.json","events_json":"https://pith.science/api/pith-number/TGG7RFUPJJRKFJTF3CCWS4EI4J/events.json","paper":"https://pith.science/paper/TGG7RFUP"},"agent_actions":{"view_html":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J","download_json":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J.json","view_paper":"https://pith.science/paper/TGG7RFUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.4062&json=true","fetch_graph":"https://pith.science/api/pith-number/TGG7RFUPJJRKFJTF3CCWS4EI4J/graph.json","fetch_events":"https://pith.science/api/pith-number/TGG7RFUPJJRKFJTF3CCWS4EI4J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J/action/storage_attestation","attest_author":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J/action/author_attestation","sign_citation":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J/action/citation_signature","submit_replication":"https://pith.science/pith/TGG7RFUPJJRKFJTF3CCWS4EI4J/action/replication_record"}},"created_at":"2026-05-18T03:55:01.529349+00:00","updated_at":"2026-05-18T03:55:01.529349+00:00"}