{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IX5XDHB3ZKQCL3CUSFYSDF45P2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"626a3158ee1fc77c2e155e8db30074480d461c0b796380fc4060582c7b049f68","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-19T06:25:21Z","title_canon_sha256":"57929c718290159ec2815890a31fbe878fdb9f4a8dd2841b4e49e76e9c5a342b"},"schema_version":"1.0","source":{"id":"1103.3757","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3757","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3757v3","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3757","created_at":"2026-05-18T03:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"IX5XDHB3ZKQC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IX5XDHB3ZKQCL3CU","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IX5XDHB3","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:1a4b4f4f9fbe5b77f4bd7d917aa81c1390cf8d44467a3cce3e7dc67354f89681","target":"graph","created_at":"2026-05-18T03:07:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce a new class of Hardy spaces $H^{\\varphi(\\cdot,\\cdot)}(\\mathbb R^n)$, called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garc\\'ia-Cuerva, Str\\\"omberg, and Torchinsky. Here, $\\varphi: \\mathbb R^n\\times [0,\\infty)\\to [0,\\infty)$ is a function such that $\\varphi(x,\\cdot)$ is an Orlicz function and $\\varphi(\\cdot,t)$ is a Muckenhoupt $A_\\infty$ weight. A function $f$ belongs to $H^{\\varphi(\\cdot,\\cdot)}(\\mathbb R^n)$ if and only if its maximal function $f^*$ is so that $x\\mapsto \\varphi(x,|f^*(x)|)$ is integr","authors_text":"Luong Dang Ky (MAPMO)","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-19T06:25:21Z","title":"New Hardy spaces of Musielak-Orlicz type and boundedness of sublinear operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3757","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7c5ff351d0b7eccb975d7877d41a3adeaa49642c5d0367fb29266b8e2f72efdb","target":"record","created_at":"2026-05-18T03:07:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"626a3158ee1fc77c2e155e8db30074480d461c0b796380fc4060582c7b049f68","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-19T06:25:21Z","title_canon_sha256":"57929c718290159ec2815890a31fbe878fdb9f4a8dd2841b4e49e76e9c5a342b"},"schema_version":"1.0","source":{"id":"1103.3757","kind":"arxiv","version":3}},"canonical_sha256":"45fb719c3bcaa025ec54917121979d7e9036b73ccf091d59bd1e3b8d2220f803","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45fb719c3bcaa025ec54917121979d7e9036b73ccf091d59bd1e3b8d2220f803","first_computed_at":"2026-05-18T03:07:32.231895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:32.231895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5AziXJ4Ov9r7b8jVlfq312Q1GyqZdPXyMgcgb9YoHfetuBfFoJgsE2zJorqNyUqND66TMLFUS4DPOjnDOv4lAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:32.232506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3757","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c5ff351d0b7eccb975d7877d41a3adeaa49642c5d0367fb29266b8e2f72efdb","sha256:1a4b4f4f9fbe5b77f4bd7d917aa81c1390cf8d44467a3cce3e7dc67354f89681"],"state_sha256":"91a52a1096f27dbfc58a144d21df4d50faa3a82b7ca8577995a708e05d782941"}