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Embedding theorems for holomorphic functions of several complex variables

Długosz R

Journal of Applied Analysis

2013

Vol. 19, nr 1

153--165

Many authors studied families XG of complex valued functions, which are holomorphic in bounded complete n-circular domains G⊂Cn and fulfill some geometric conditions. The above functions were applied later to research families of locally biholomorphic mappings in Cn. In this paper we consider a problem of inclusions between a few of such families XG and families MKG, k=2, 3, …, which are defined by applying a function decomposition with respect to the group of kth roots of unity.

New properties of some families of holomorphic functions of several complex variables

Leś-Bomba E., Liczberski P.

Demonstratio Mathematica

2009

Vol. 42, nr 3

491-503

The paper concerns holomorphic functions in complete bounded n-circular domains of the space Cn and presents some properties of the above mentioned functions belonging to the families described by some geometrical or analytical conditions. This subject has been considered by many mathematicans, for example I.I. Bavrin, K. Dobrowolska, I. Dziubiński, S. Fukui, Z. J. Jakubowski, J. Kamiński, A. Marchlewska, Y. Michiwaki, J. A. Pfaltzgraff, R. Sitarski, T. J. Suffridge, J. Stankiewicz, I. Weinberg, A. Wrzesień, Ł. Żywień and the authors.