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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.09303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-25T22:31:51Z","cross_cats_sorted":[],"title_canon_sha256":"231c49197b2b7b750034c1d84d0739265aca3321f04f5517c923376505a2370d","abstract_canon_sha256":"b4941f88cb46ba57dd547cfbf27c16cce8c5caf5515388e5b75b8c20f934610d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:36.079667Z","signature_b64":"0f484t3aqAnWCHheqQYTqKcc9Ss2o1pJBdJtOimxxXNS2UH5gnUs6NkuqeEj+9TqfrqVib2LfWjBT9psB8tGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ffb3e3364e02b2b8c6cb16e82af0c761345e65b286b68851dd4e1b38e46360e","last_reissued_at":"2026-05-18T00:29:36.079086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:36.079086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"T1 theorem for Campanato spaces on domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andrei V. 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