{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N75T4M3E4AVSXDDMWFXIFLYMOY","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":"b4941f88cb46ba57dd547cfbf27c16cce8c5caf5515388e5b75b8c20f934610d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-25T22:31:51Z","title_canon_sha256":"231c49197b2b7b750034c1d84d0739265aca3321f04f5517c923376505a2370d"},"schema_version":"1.0","source":{"id":"1711.09303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09303","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09303v1","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09303","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"N75T4M3E4AVS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N75T4M3E4AVSXDDM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N75T4M3E","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:706eaf8593fbbd4d06bbb079f874c7cf88c60f7af52c8ab9a88494915a4c817b","target":"graph","created_at":"2026-05-18T00:29:36Z","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":"Given a Lipschitz domain $D\\subset \\mathbb{R}^d,$ a Calder\\'on-Zygmund operator $T$ and a modulus of continuity $\\omega(x),$ we solve a problem when the restricted operator $T_Df=T(f\\chi_D)\\chi_D$ sends the Campanato space $\\mathcal{C}_\\omega(D)$ into itself. The solution is a T1 type sufficient and necessary condition for the characteristic function $\\chi_D$ of $D$:\n  $$(T\\chi_D)\\chi_D \\in \\mathcal{C}_{\\tilde{\\omega}}(D),$$ assumed $\\tilde{\\omega}(x)= \\omega(x)/\\int_x^1 \\omega(t)dt/t.$ To check the hypotheses of T1 theorem we need extra restrictions on both the boundary of $D$ and the operato","authors_text":"Andrei V. Vasin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-25T22:31:51Z","title":"T1 theorem for Campanato spaces on domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09303","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":"sha256:669b6d3bc178a987e1e01880ac9832528193c2d2c46a617bff3aba849caf6144","target":"record","created_at":"2026-05-18T00:29:36Z","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":"b4941f88cb46ba57dd547cfbf27c16cce8c5caf5515388e5b75b8c20f934610d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-25T22:31:51Z","title_canon_sha256":"231c49197b2b7b750034c1d84d0739265aca3321f04f5517c923376505a2370d"},"schema_version":"1.0","source":{"id":"1711.09303","kind":"arxiv","version":1}},"canonical_sha256":"6ffb3e3364e02b2b8c6cb16e82af0c761345e65b286b68851dd4e1b38e46360e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ffb3e3364e02b2b8c6cb16e82af0c761345e65b286b68851dd4e1b38e46360e","first_computed_at":"2026-05-18T00:29:36.079086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:36.079086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0f484t3aqAnWCHheqQYTqKcc9Ss2o1pJBdJtOimxxXNS2UH5gnUs6NkuqeEj+9TqfrqVib2LfWjBT9psB8tGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:36.079667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:669b6d3bc178a987e1e01880ac9832528193c2d2c46a617bff3aba849caf6144","sha256:706eaf8593fbbd4d06bbb079f874c7cf88c60f7af52c8ab9a88494915a4c817b"],"state_sha256":"95783e0e34625fb7a205d99e5a51f5f553c3b9e24b5315d3faaeb941ff06eedf"}