{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PCYHE222W6QEP6FYC4VR5VZD4T","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":"5704292547e97e923870b18153c66b4b2728ca0be3a35d1bfd99ffe47f8c4ed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-17T21:10:28Z","title_canon_sha256":"e3d376bf93ecaf4c8ed6ebecf03a2019a4e94e7d20f43404f8d5f86d27f570fc"},"schema_version":"1.0","source":{"id":"1207.4217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4217","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4217v1","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4217","created_at":"2026-05-18T03:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"PCYHE222W6QE","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PCYHE222W6QEP6FY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PCYHE222","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:275d7a72c7998c06b0d19f92d0d2097a4c118534e2e70cdd462e99132160b73f","target":"graph","created_at":"2026-05-18T03:50:47Z","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 introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of $\\mathcal{R}_s$-sectorial operators, which in turn is based on the notion of $\\mathcal{R}_s$-bounded sets of operators introduced by Lutz Weis, we obtain a neat theory including equivalence of various norms and a precise description of real and complex interpolation spaces. Another main result of this article is that an $\\mathcal{R}_s$-sectorial operator always has a bounded $H^\\inft","authors_text":"Alexander Ullmann, Peer Christian Kunstmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-17T21:10:28Z","title":"Rs-sectorial operators and generalized Triebel-Lizorkin spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4217","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:fe9686c19dd8658e6948253ada111551579ec5ca417d7023f23586555d31c007","target":"record","created_at":"2026-05-18T03:50:47Z","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":"5704292547e97e923870b18153c66b4b2728ca0be3a35d1bfd99ffe47f8c4ed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-17T21:10:28Z","title_canon_sha256":"e3d376bf93ecaf4c8ed6ebecf03a2019a4e94e7d20f43404f8d5f86d27f570fc"},"schema_version":"1.0","source":{"id":"1207.4217","kind":"arxiv","version":1}},"canonical_sha256":"78b0726b5ab7a047f8b8172b1ed723e4f0bdf0356917b31bb1ff8ef392de349b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78b0726b5ab7a047f8b8172b1ed723e4f0bdf0356917b31bb1ff8ef392de349b","first_computed_at":"2026-05-18T03:50:47.320477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:47.320477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SUEe7SFzR3aCqzxj+1WXzCvZJ2iObW9i9Y/NkPKL1rf3WCh7p/MCzzE1b4ztu4iREydO+ru01y5dvP6s90jpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:47.321118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe9686c19dd8658e6948253ada111551579ec5ca417d7023f23586555d31c007","sha256:275d7a72c7998c06b0d19f92d0d2097a4c118534e2e70cdd462e99132160b73f"],"state_sha256":"1aeb81336a7a5f2655e0edf5fd24e7550850231bc3c8b35f520d7bfc84ed1442"}