Geodesic
Conformal mappings of circular domains on finitely-connected non-Smirnov type domains
Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 3-17

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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. 
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F. G. Avkhadiev; P. L. Shabalin. Conformal mappings of circular domains on  finitely-connected non-Smirnov type domains. Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a0/