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Sbornik: Mathematics, 2018, Volume 209, Issue 12, Pages 1728–1744
DOI: https://doi.org/10.1070/SM8655 (Mi sm8655) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
English version PDF (526 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM8655
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).
Received: 24.12.2015 and 18.09.2018
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 30D60
Language: English
Original paper language: Russian
Citation: R. A. Gaisin, “A universal criterion for quasi-analytic classes in Jordan domains”, Sb. Math., 209:12 (2018), 1728–1744
Citation in format AMSBIB
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\paper A~universal criterion for quasi-analytic classes in Jordan domains
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\vol 209
\issue 12
\pages 1728--1744
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  • https://www.mathnet.ru/eng/sm8655
  • https://doi.org/10.1070/SM8655
  • https://www.mathnet.ru/eng/sm/v209/i12/p57
    • This publication is cited in the following 1 articles:
    1. A. V. Lutsenko, I. Kh. Musin, “On space of holomorphic functions with boundary smoothness and its dual”, Ufa Math. J., 13:3 (2021), 80–94  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:384
    Russian version PDF:39
    English version PDF:14
    References:65
    First page:13
     
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