{"paper":{"title":"Correlation of boundary behavior of conjugate harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Vladimir Ryazanov","submitted_at":"2017-10-01T09:30:16Z","abstract_excerpt":"It is established that if a harmonic function $u$ on the unit disk $\\mathbb D$ in $\\mathbb C$ has angular limits on a measurable set $E$ of the unit circle $\\partial\\mathbb D$, then its conjugate harmonic function $v$ in $\\mathbb D$ also has angular limits a.e. on $E$ and both boundary functions are finite a.e. and measurable on $E$. The result is extended to arbitrary Jordan domains with rectifiable boundaries in terms of angular limits and of the natural parameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00323","kind":"arxiv","version":3},"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"}