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Matematicheskie Zametki, 2011, Volume 90, Issue 4, Pages 501–516
DOI: https://doi.org/10.4213/mzm8760 (Mi mzm8760) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Behavior of Conformal Maps of Domains Near Convex Boundary Arcs

E. P. Dolzhenkoa, S. V. Kolesnikovb

a M. V. Lomonosov Moscow State University
b Ivanovo State University
Full-text PDF (566 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm8760
Abstract: The behavior of the derivatives of conformal maps of the unit disk onto simply connected domains in the complex plane whose boundaries contain convex or concave attainable arcs, as well as the behavior of the derivatives of the inverse maps, is studied. It is proved that these derivatives exist and are bounded on the corresponding arcs and near them; a criterion for their continuity at points of these arcs is stated and proved.
Keywords: analytic conformal map, simply connected domain, Jordan arc, Poisson integral, convex (concave) attainable boundary arc, boundary arc, angular boundary limit, angular derivative, Hardy class, Schwarz integral, Borel measure.
Received: 20.04.2010
Revised: 24.01.2011
English version:
Mathematical Notes, 2011, Volume 90, Issue 4, Pages 485–497
DOI: https://doi.org/10.1134/S0001434611090197
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: E. P. Dolzhenko, S. V. Kolesnikov, “The Behavior of Conformal Maps of Domains Near Convex Boundary Arcs”, Mat. Zametki, 90:4 (2011), 501–516; Math. Notes, 90:4 (2011), 485–497
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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