{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FBXVGKMJSJMJ2QX7U73ILFVSVV","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":"24b2f360a7c9b32ae966eca8deee058f46d574bd810206703397fb1d0f99a348","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-26T15:38:03Z","title_canon_sha256":"49c6726efb9e59b837b7bb73302b452ccf166e8095a1453becfb90a9e490c179"},"schema_version":"1.0","source":{"id":"1907.11633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11633","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11633v1","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11633","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"FBXVGKMJSJMJ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FBXVGKMJSJMJ2QX7","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FBXVGKMJ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:b90ca185ec708a390ce961f79210f503c80a6bea46df5c60b6828d83484ea962","target":"graph","created_at":"2026-05-17T23:39:28Z","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":"Recently, in \\cite{GXHTM}, the authors established $L^p$-boundedness of vector-valued $q$-variational inequalities for averaging operators which take values in the Banach space satisfying martingale cotype $q$ property. In this paper, we prove that martingale cotype $q$ property is also necessary for the vector-valued $q$-variational inequalities, which is a question left open. Moreover, we characterize UMD property and martingale cotype $q$ property in terms of vector valued $q$-variational inequalities for Hilbert transform.","authors_text":"Guixiang Hong, Tao Ma, Wei Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-26T15:38:03Z","title":"Vector-valued $q$-variational inequalities for averaging operators and Hilbert transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11633","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":"sha256:6c49bdcf47ccce2500f28024b42914bef2703611e239fa451d9a725bc014262c","target":"record","created_at":"2026-05-17T23:39:28Z","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":"24b2f360a7c9b32ae966eca8deee058f46d574bd810206703397fb1d0f99a348","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-26T15:38:03Z","title_canon_sha256":"49c6726efb9e59b837b7bb73302b452ccf166e8095a1453becfb90a9e490c179"},"schema_version":"1.0","source":{"id":"1907.11633","kind":"arxiv","version":1}},"canonical_sha256":"286f53298992589d42ffa7f68596b2ad74c7367602e96251cd55c0e9d61a2a3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"286f53298992589d42ffa7f68596b2ad74c7367602e96251cd55c0e9d61a2a3d","first_computed_at":"2026-05-17T23:39:28.445131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:28.445131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EDw4NsiWelAmp3Kvbqq5SuGqAejwgj1Iyo/ZGGkyxBBxs5kGhh/BtU2ph51p0yJaXONL+W2FvrmAVscFD8L7Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:28.445665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c49bdcf47ccce2500f28024b42914bef2703611e239fa451d9a725bc014262c","sha256:b90ca185ec708a390ce961f79210f503c80a6bea46df5c60b6828d83484ea962"],"state_sha256":"54f25238b17a10664b83b5ae2bbe8d563351487f7bcee43b079d1a0ea0500150"}