{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MUCAJYQOZMW5C4YMTUFMKZ2PVA","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":"cb69635f29b70e181a4e542807a4a7fac182f8cf4b1b161011e21a05be684967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-07T09:59:10Z","title_canon_sha256":"c0cb07a0a7a797aaf09f38a4120fc22a02f6e21d156543ba49d65e4c8962a93b"},"schema_version":"1.0","source":{"id":"1807.02640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02640","created_at":"2026-05-18T00:11:16Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02640v1","created_at":"2026-05-18T00:11:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02640","created_at":"2026-05-18T00:11:16Z"},{"alias_kind":"pith_short_12","alias_value":"MUCAJYQOZMW5","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MUCAJYQOZMW5C4YM","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MUCAJYQO","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:0a67755f8ba6a3bc213a37470e4057b7c39479c8b4284b1abecaa3ea8747a419","target":"graph","created_at":"2026-05-18T00:11:16Z","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":"For a normalized root system $R$ in $\\mathbb R^N$ and a multiplicity function $k\\geq 0$ let $\\mathbf N=N+\\sum_{\\alpha \\in R} k(\\alpha)$. Denote by $dw(\\mathbf x)=\\prod_{\\alpha\\in R}|\\langle \\mathbf x,\\alpha\\rangle|^{k(\\alpha)}\\, d\\mathbf x $ the associated measure in $\\mathbb R^N$. Let $\\mathcal F$ stands for the Dunkl transform. Given a bounded function $m$ on $\\mathbb R^N$, we prove that if there is $s>\\mathbf N$ such that $m$ satisfies the classical H\\\"ormander condition with the smoothness $s$, then the multiplier operator $\\mathcal T_mf=\\mathcal F^{-1}(m\\mathcal Ff)$ is of weak type $(1,1","authors_text":"Agnieszka Hejna, Jacek Dziuba\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-07T09:59:10Z","title":"H\\\"ormander's multiplier theorem for the Dunkl transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02640","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":"sha256:6e667555ec33e6867543851a20daa37f3a87004b2c41d4fa8806cace9e609a32","target":"record","created_at":"2026-05-18T00:11:16Z","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":"cb69635f29b70e181a4e542807a4a7fac182f8cf4b1b161011e21a05be684967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-07T09:59:10Z","title_canon_sha256":"c0cb07a0a7a797aaf09f38a4120fc22a02f6e21d156543ba49d65e4c8962a93b"},"schema_version":"1.0","source":{"id":"1807.02640","kind":"arxiv","version":1}},"canonical_sha256":"650404e20ecb2dd1730c9d0ac5674fa80d45b09c82ca48206e112a8956c59b40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"650404e20ecb2dd1730c9d0ac5674fa80d45b09c82ca48206e112a8956c59b40","first_computed_at":"2026-05-18T00:11:16.457239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:16.457239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BwI81cdSOGikAtZSiO5DJLkr6uC8L1VJjG8XSMwFKeLvUnzpCfFIvlGCyo+676ft0Bo44AXZVL4Bodm90gXACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:16.457891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e667555ec33e6867543851a20daa37f3a87004b2c41d4fa8806cace9e609a32","sha256:0a67755f8ba6a3bc213a37470e4057b7c39479c8b4284b1abecaa3ea8747a419"],"state_sha256":"04cddb3ab0e240cb1af5bda10f57cf855806b72884cf88bf559d6b99eed02d4d"}