{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LEEVJHBCPGFRSODYOMQ3NBJRP2","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":"0a58cce476a8ed598b919576bbc1c56ce6a7a074e00f070d44f09af0de1d0b24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-30T13:42:09Z","title_canon_sha256":"7e7814674ebe431c109e810ad235e2df875434c6b7cf64ae632a0e4151c2b576"},"schema_version":"1.0","source":{"id":"1404.7721","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7721","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7721v2","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7721","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"LEEVJHBCPGFR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LEEVJHBCPGFRSODY","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LEEVJHBC","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:d4d16d43564c097bdfa39c252756f044f2a7b1f78eb637f7312265d769acf66c","target":"graph","created_at":"2026-05-18T02:52:13Z","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 give a characterization of $BMO^\\alpha$-martingale spaces by using fractional Carleson measures. We get the boudedness of martingale transform and square function on $BMO^\\alpha$-martingale spaces easily by using this characterization. We also proved the martingale version of Carleson's inequality related with $BMO^\\alpha$-martingales.","authors_text":"Chao Zhang, Peide Liu, Wei Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-30T13:42:09Z","title":"A Characterization of BMO^\\alpha-martingale spaces by fractional Carleson measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7721","kind":"arxiv","version":2},"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:b293d8578b1178ec16a5f5733b18f2911d7e2af3bb09b0c0a68f7b2c19372f76","target":"record","created_at":"2026-05-18T02:52:13Z","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":"0a58cce476a8ed598b919576bbc1c56ce6a7a074e00f070d44f09af0de1d0b24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-30T13:42:09Z","title_canon_sha256":"7e7814674ebe431c109e810ad235e2df875434c6b7cf64ae632a0e4151c2b576"},"schema_version":"1.0","source":{"id":"1404.7721","kind":"arxiv","version":2}},"canonical_sha256":"5909549c22798b1938787321b685317eabe49e0df87fa27314520565d7f0f1e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5909549c22798b1938787321b685317eabe49e0df87fa27314520565d7f0f1e9","first_computed_at":"2026-05-18T02:52:13.817379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:13.817379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OpYtIO/ygkuk4NCGOWImVp7bNLbNP4dkFWlUHlhHn1osBaVVowVn1Ue/suQNIwcIffF8QgRkRRSPxZm/hv18AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:13.818010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7721","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b293d8578b1178ec16a5f5733b18f2911d7e2af3bb09b0c0a68f7b2c19372f76","sha256:d4d16d43564c097bdfa39c252756f044f2a7b1f78eb637f7312265d769acf66c"],"state_sha256":"8fdfc80bbf010e2865a7ce9e78c635f0c9c7ff7f0c7852df38e028ae26473b31"}