{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A7S2TEUBVN46LR5M25VGP2CUNS","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":"9be537ea7e01dd6aa12717144893203e9b4e134015e275e1f7cf6b7d601ff46d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-27T06:28:44Z","title_canon_sha256":"99a8df0f2648df4c1478f162baf890ba9c1450890cb66c52a1194e0046817e4a"},"schema_version":"1.0","source":{"id":"1209.6133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6133","created_at":"2026-05-18T03:44:35Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6133v1","created_at":"2026-05-18T03:44:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6133","created_at":"2026-05-18T03:44:35Z"},{"alias_kind":"pith_short_12","alias_value":"A7S2TEUBVN46","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A7S2TEUBVN46LR5M","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A7S2TEUB","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:a9401825a60daf8cdcb7baa1ee737212857cc76ca8876438dac78a7f83ccf632","target":"graph","created_at":"2026-05-18T03:44:35Z","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":"In a previous paper the boundedness properties of Riesz Potentials, Bessel potentials and Fractional Derivatives were studied in detail on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\\alpha}(\\gamma_d)$. In this paper we will continue our study proving the boundedness of those operators on Gaussian Triebel-Lizorkin spaces $F_{p,q}^{\\alpha}(\\gamma_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.","authors_text":"A. Eduardo Gatto, Ebner Pineda, Wilfredo Urbina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-27T06:28:44Z","title":"Riesz Potentials, Bessel Potentials and Fractional Derivatives on Triebel-Lizorkin spaces for the Gaussian Measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6133","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:d73916f474342df16e4fbd92162c5a40f016989374cb48a9dc957d6af2bb02a8","target":"record","created_at":"2026-05-18T03:44:35Z","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":"9be537ea7e01dd6aa12717144893203e9b4e134015e275e1f7cf6b7d601ff46d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-27T06:28:44Z","title_canon_sha256":"99a8df0f2648df4c1478f162baf890ba9c1450890cb66c52a1194e0046817e4a"},"schema_version":"1.0","source":{"id":"1209.6133","kind":"arxiv","version":1}},"canonical_sha256":"07e5a99281ab79e5c7acd76a67e8546c88b059cd2cb54e881f375709c728b6d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07e5a99281ab79e5c7acd76a67e8546c88b059cd2cb54e881f375709c728b6d6","first_computed_at":"2026-05-18T03:44:35.264410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:35.264410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"26GvrcBpEUXveO+474w1ot7ehxFeYc8k2B9iPGXzkE/LQ1hYqOETi0oMNay2/Nn+ytSZ+AmMtUSRGaCDe8FIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:35.265182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.6133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d73916f474342df16e4fbd92162c5a40f016989374cb48a9dc957d6af2bb02a8","sha256:a9401825a60daf8cdcb7baa1ee737212857cc76ca8876438dac78a7f83ccf632"],"state_sha256":"78a5b68036273b4aa228383acb361a7115137a8e8a21e06efba82da489fe9644"}