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Mat. Sb., 2018, Volume 209, Number 12, Pages 57–74 (Mi msb8655)  

A universal criterion for quasi-analytic classes in Jordan domains

R. A. Gaisin

Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences

Abstract: Carleman classes in Jordan domains in the complex plane are investigated. A criterion for regular Carleman classes to be quasi-analytic is established, which is universal in a certain sense for all weakly uniform domains. The proof is based on a solution of the Dirichlet problem with unbounded boundary function, and a result on bounds for the harmonic measure due to Beurling plays a substantial role.
Bibliography: 20 titles.

Keywords: quasi-analytic classes in Jordan domains, harmonic measure, Dirichlet problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00095-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 18-01-00095-a).


DOI: https://doi.org/10.4213/sm8655

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English version:
Sbornik: Mathematics, 2018, 209:12, 1728–1744

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: 30D60
Received: 24.12.2015 and 18.09.2018

Citation: R. A. Gaisin, “A universal criterion for quasi-analytic classes in Jordan domains”, Mat. Sb., 209:12 (2018), 57–74; Sb. Math., 209:12 (2018), 1728–1744

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