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

Authors

  • F.G. Avkhadiev
    Kazan Federal University, Kremlevskaya str., 18, 420008, Kazan, Russia
  • P.L. Shabalin
    Kazan State University of Architecture and Engineering, Zelenaya str., 1, 420043, Kazan, Russia

DOI:

https://doi.org/10.13108/2017-9-1-3

Keywords:

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

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.

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Published

20.03.2017

Issue

Vol. 9 No. 1 (2017): Ufa Mathematical Journal 2017, volume 9 , issue 1

Section

Article