{"paper":{"title":"On the Cauchy transform of weighted Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sergei Merenkov","submitted_at":"2013-05-18T02:18:35Z","abstract_excerpt":"The problem of describing the range of a Bergman space B_2(G) under the Cauchy transform K for a Jordan domain G was solved by Napalkov (Jr) and Yulmukhametov. It turned out that K(B_2(G))=B_2^1(C\\bar G) if and only if G is a quasidisk; here B_2^1(C\\bar G) is the Dirichlet space of the complement of \\bar G. The description of K(B_2(G)) for an integrable Jordan domain is given in [S. Merenkov, \"On the Cauchy transform of the Bergman space\", Mat. Fiz. Anal. Geom., 7 (2000), no. 1, 119-127]. In the present paper we give a description of K(B_2(G,\\omega)) analogous to the one given in [S. Merenkov,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4217","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"}