{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2G5FBTCPSUHBUSGIBN733JKTES","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":"0dbfe673a874c86183fdf8d31fd8784f19a63dacdc019a13b1687679769ce2eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-15T21:31:46Z","title_canon_sha256":"1b1b86e8dfbaa6bd9d81194cc5d3b002e8af9370f232facd7346be68e155a493"},"schema_version":"1.0","source":{"id":"1112.3678","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3678","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3678v2","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3678","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"2G5FBTCPSUHB","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2G5FBTCPSUHBUSGI","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2G5FBTCP","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:71caffcdd95ccbbe50c149538926ae295069eed0a6b556eabc47753f1aabe516","target":"graph","created_at":"2026-05-18T00:26:52Z","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 provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces $ \\mathcal{S}_0(\\mathbb{R}^n) $ and $ \\mathcal{S}(\\mathbb{H}^{n+1})$. We then introduce and study a new class of weighted H\\\"older-Zygmund spaces, where the weights are regularly varying functions. The analysis of these spaces is carried out via the wavelet transform and generalized Littlewood-Paley pairs.","authors_text":"Dusan Rakic, Jasson Vindas, Stevan Pilipovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-15T21:31:46Z","title":"New classes of weighted H\\\"older-Zygmund spaces and the wavelet transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3678","kind":"arxiv","version":2},"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":"sha256:328bc4c5aff552df8678c67ae1782cc89d4a59e112e2930f937abba99e79c97c","target":"record","created_at":"2026-05-18T00:26:52Z","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":"0dbfe673a874c86183fdf8d31fd8784f19a63dacdc019a13b1687679769ce2eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-15T21:31:46Z","title_canon_sha256":"1b1b86e8dfbaa6bd9d81194cc5d3b002e8af9370f232facd7346be68e155a493"},"schema_version":"1.0","source":{"id":"1112.3678","kind":"arxiv","version":2}},"canonical_sha256":"d1ba50cc4f950e1a48c80b7fbda55324915339c6934126a8bee53d79f63de838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1ba50cc4f950e1a48c80b7fbda55324915339c6934126a8bee53d79f63de838","first_computed_at":"2026-05-18T00:26:52.333913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:52.333913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KkeJri383bRx0Wr7TO1/9uy2kmg1h6xxxBUu3Bf+TF+Bp+F1KKsBf83PGVqDIgWFGcNlKZG2xIRgAhcmcT1wAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:52.334650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3678","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:328bc4c5aff552df8678c67ae1782cc89d4a59e112e2930f937abba99e79c97c","sha256:71caffcdd95ccbbe50c149538926ae295069eed0a6b556eabc47753f1aabe516"],"state_sha256":"d2364a0a3424f8ef1a26e0a66f41ee6b7b3e0ea0ceabcb79699abea9a226047f"}