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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 1, Pages 3–17 (Mi ufa360)  

Conformal mappings of circular domains on finitely-connected non-Smirnov type domains

F. G. Avkhadieva, P. L. Shabalinb

a Kazan Federal University, Kremlevskaya str., 18, 420008, Kazan, Russia
b Kazan State University of Architecture and Engineering, Zelenaya str., 1, 420043, Kazan, Russia

Abstract: We consider a canonical factorization and integral representation for the derivatives of the conformal mappings of circular domains on finitely-connected non-Smirnov type domains. By means of the functions in the Zygmund class, we obtain the conditions for the global univalence. Earlier similar results were obtained by a series of authors just for simply-connected domains.

Keywords: non-Smirnov type domain, Zygmun condition, Schwarz operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00371-а
The work is supported by RFBR (project no. 14-01-00371-a).


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English version:
Ufa Mathematical Journal, 2017, 9:1, 3–17 (PDF, 532 kB); https://doi.org/10.13108/2017-9-1-3

Document Type: Article
UDC: 517.54
MSC: 30C45, 30C55, 30C62, 31A20
Received: 25.07.2016

Citation: F. G. Avkhadiev, P. L. Shabalin, “Conformal mappings of circular domains on finitely-connected non-Smirnov type domains”, Ufimsk. Mat. Zh., 9:1 (2017), 3–17; Ufa Math. Journal, 9:1 (2017), 3–17

Citation in format AMSBIB
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\paper Conformal mappings of circular domains on  finitely-connected non-Smirnov type domains
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\yr 2017
\vol 9
\issue 1
\pages 3--17
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\transl
\jour Ufa Math. Journal
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