{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BDGZ4KSQWRCJMEMWCWEKZFQGJC","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":"a9131beae213510c6f16399edb7989d0ce9cada44526b47ca2fa542ef1de8a12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-13T13:46:10Z","title_canon_sha256":"8998d353682badce1a9561837ef9d0b6ae678b4ae8a23c0189cb05c611d800e5"},"schema_version":"1.0","source":{"id":"1303.3159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3159","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3159v1","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3159","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"BDGZ4KSQWRCJ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BDGZ4KSQWRCJMEMW","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BDGZ4KSQ","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:0034c69adbc482c169910ab02e8d1f6a1c885243d1bfd5efd83ff7ebb4256294","target":"graph","created_at":"2026-05-18T01:12:43Z","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":"In this paper we consider square functions (also called Littlewood-Paley g-functions) associated to Hankel convolutions acting on functions in the Bochner-Lebesgue space $L^p((0,\\infty),B)$, where $B$ is a UMD Banach space. As special cases we study square functions defined by fractional derivatives of the Poisson semigroup for the Bessel operator $\\Delta_\\lambda=-x^{-\\lambda}\\frac{d}{dx}x^{2\\lambda}\\frac{d}{dx}x^{-\\lambda}$, $\\lambda >0$. We characterize the UMD property for a Banach space $B$ by using $L^p((0,\\infty),B)$-boundedness properties of g-functions defined by Bessel-Poisson semigro","authors_text":"Alejandro J. Castro, Jorge J. Betancor, Lourdes Rodriguez-Mesa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-13T13:46:10Z","title":"Square functions and spectral multipliers for Bessel operators in UMD spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3159","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:c21be405e933a7b26466dc479bf2806f3f43f6c5d695e0b556d819f73418786a","target":"record","created_at":"2026-05-18T01:12:43Z","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":"a9131beae213510c6f16399edb7989d0ce9cada44526b47ca2fa542ef1de8a12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-13T13:46:10Z","title_canon_sha256":"8998d353682badce1a9561837ef9d0b6ae678b4ae8a23c0189cb05c611d800e5"},"schema_version":"1.0","source":{"id":"1303.3159","kind":"arxiv","version":1}},"canonical_sha256":"08cd9e2a50b4449611961588ac960648a385f627c5352320527276fea0467c7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08cd9e2a50b4449611961588ac960648a385f627c5352320527276fea0467c7e","first_computed_at":"2026-05-18T01:12:43.918826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:43.918826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDz7JG96K2Lto0mgrpQE1e7oXmZKDZsE7aH50Exp77kDHJJBOHoC08XST17fdRr1Cg9xP+o6OeeHjn0bLykjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:43.919178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c21be405e933a7b26466dc479bf2806f3f43f6c5d695e0b556d819f73418786a","sha256:0034c69adbc482c169910ab02e8d1f6a1c885243d1bfd5efd83ff7ebb4256294"],"state_sha256":"7930550322ad0bc3d79be3ebc6c91aa9b811d780a342538c1c6bbf9a0d43b2f9"}