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

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.