{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HKZA4PRUPIPEX5B5NXHXBCHQB3","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":"a68ee57baa2ed9963913facddaa1bffe61a29cddd3e3c8ee476639fe886692e2","cross_cats_sorted":["math.FA","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-23T15:05:43Z","title_canon_sha256":"f6d4df7a1ea6d009150e449b39c43ebbe5ba7122a15a035636f9c7667a87e01e"},"schema_version":"1.0","source":{"id":"1204.5082","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5082","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5082v3","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5082","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"HKZA4PRUPIPE","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HKZA4PRUPIPEX5B5","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HKZA4PRU","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:bbacede6fa1e1cdca31dcb8874cf8ecb0aa814215c0b07a7cd4e06bb5d936ea7","target":"graph","created_at":"2026-05-18T03:56:44Z","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":"Let (M,\\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\\mu) with standard assumptions. We prove a H_1-BMO duality theory with assumptions only on T_t. The BMO is defined as spaces of functions f such that the L_\\infty norm of sup_tT_t|f-T_tf|^2 is finite. The H1 is defined by square functions of P. A. Meyer's gradient form. Our argument does not rely on any geometric/metric structure of M nor on the kernel of the semigroups of operators. This abstract argument allows to extend our main results to the noncommutative setting, e.g. the case where L","authors_text":"Tao Mei","cross_cats":["math.FA","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-23T15:05:43Z","title":"An H1-BMO duality theory for semigroups of operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5082","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":"sha256:505de252d1eab1d0c55081d3f339a47da219fa8b2f2e8003ffc567c8a66ef3f0","target":"record","created_at":"2026-05-18T03:56:44Z","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":"a68ee57baa2ed9963913facddaa1bffe61a29cddd3e3c8ee476639fe886692e2","cross_cats_sorted":["math.FA","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-23T15:05:43Z","title_canon_sha256":"f6d4df7a1ea6d009150e449b39c43ebbe5ba7122a15a035636f9c7667a87e01e"},"schema_version":"1.0","source":{"id":"1204.5082","kind":"arxiv","version":3}},"canonical_sha256":"3ab20e3e347a1e4bf43d6dcf7088f00ed1717be76f5d0bf02243d013d4cea8c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ab20e3e347a1e4bf43d6dcf7088f00ed1717be76f5d0bf02243d013d4cea8c6","first_computed_at":"2026-05-18T03:56:44.681551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:44.681551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oJ2ONowANZoFRiHD5BtFFiGyyDgqy8ockPo8AH8VMs99FgAr9v2+rptmsy8sr9yFFPMr6DtUwN3wmkKeNlgmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:44.682027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5082","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:505de252d1eab1d0c55081d3f339a47da219fa8b2f2e8003ffc567c8a66ef3f0","sha256:bbacede6fa1e1cdca31dcb8874cf8ecb0aa814215c0b07a7cd4e06bb5d936ea7"],"state_sha256":"a22ea6c2f9828c12df33717849727e7472290dbf02b64bebce33d910fd87e12e"}