{"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. Vasin","submitted_at":"2017-11-25T22:31:51Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09303","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}