{"paper":{"title":"Universal conformal weights on Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.Ukhlov, V.Gol'dshtein","submitted_at":"2013-02-17T10:49:24Z","abstract_excerpt":"The Riemann Mapping Theorem states existence of a conformal homeomorphism $\\varphi$ of a simply connected plane domain $\\Omega\\subset\\mathbb C$ with non-empty boundary onto the unit disc $\\mathbb D\\subset \\mathbb C$. In the first part of the paper we study embeddings of Sobolev spaces $\\overset{\\circ}{W_{p}^{1}}(\\Omega)$ into weighted Lebesgue spaces $L_{q}(\\Omega,h)$ with an {}\"universal\" weight that is Jacobian of $\\varphi$ i.e. $h(z):=J(z,\\varphi)=| \\varphi'(z)|^2$. Weighted Lebesgue spaces with such weights depend only on a conformal structure of $\\Omega$. By this reason we call the weight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4054","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"}