{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YUMBTRHTBFKCPHM453HGGUEFGS","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":"03121bb3d63ef0de5a184e5fb3e36a43f757e1ae7469fe6d671a2b42f63ca6d6","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-11T13:26:05Z","title_canon_sha256":"75bcfd0ff0c72e7e484edb303849763be88e7d70ed2d8d787a8c6fdea597faf6"},"schema_version":"1.0","source":{"id":"1810.05007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05007","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05007v1","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05007","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"YUMBTRHTBFKC","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YUMBTRHTBFKCPHM4","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YUMBTRHT","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:6a418d407554bd157c2c419f6b5bdcbcf0206f59b904a49e96bde15942cd5a32","target":"graph","created_at":"2026-05-18T00:03:35Z","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 $(\\Omega,\\mathcal{F},\\mathbb{P})$ be a probability space and $\\varphi:\\ \\Omega\\times[0,\\infty)\\to[0,\\infty)$ be a Musielak-Orlicz function. In this article, the authors prove that the Doob maximal operator is bounded on the Musielak-Orlicz space $L^{\\varphi}(\\Omega)$. Using this and extrapolation method, the authors then establish a Fefferman-Stein vector-valued Doob maximal inequality on $L^{\\varphi}(\\Omega)$. As applications, the authors obtain the dual version of the Doob maximal inequality and the Stein inequality for $L^{\\varphi}(\\Omega)$, which are new even in weighted Orlicz spaces.","authors_text":"Dachun Yang, Ferenc Weisz, Guangheng Xie, Yong Jiao","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-11T13:26:05Z","title":"New Martingale Inequalities and Applications to Fourier Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05007","kind":"arxiv","version":1},"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:c7a29f3346d8407cc05e04a7c235e83a79668dd4a09df4ae315ca8e9fe4ce572","target":"record","created_at":"2026-05-18T00:03:35Z","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":"03121bb3d63ef0de5a184e5fb3e36a43f757e1ae7469fe6d671a2b42f63ca6d6","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-11T13:26:05Z","title_canon_sha256":"75bcfd0ff0c72e7e484edb303849763be88e7d70ed2d8d787a8c6fdea597faf6"},"schema_version":"1.0","source":{"id":"1810.05007","kind":"arxiv","version":1}},"canonical_sha256":"c51819c4f30954279d9ceece635085348732c3f2dff29d7013d6aa481a4e08e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c51819c4f30954279d9ceece635085348732c3f2dff29d7013d6aa481a4e08e2","first_computed_at":"2026-05-18T00:03:35.269589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:35.269589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vaIlP9mSKbg/YRey8rnFa5e+Z3BKy4ML/OhwRvdm+ZdY6l0ExexroeeZXnCrekJJDJRihvIgrenxxcNNI7mIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:35.270093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a29f3346d8407cc05e04a7c235e83a79668dd4a09df4ae315ca8e9fe4ce572","sha256:6a418d407554bd157c2c419f6b5bdcbcf0206f59b904a49e96bde15942cd5a32"],"state_sha256":"b27ef7c4b8ec48a9ac597ab34c445ff03488ffc96e13b79486785bc31af9446c"}