Embedding theorems and extremal problems for holomorphic functions on circular domains of C-n

作者：Dlugosz Renata^*; Les Edyta

来源：Complex Variables and Elliptic Equations, 2014, 59(6): 883-899.

DOI：10.1080/17476933.2013.794139

• holomorphic functions of several complex variables
• n-circular domains in C-n
• Minkowski function
• Bavrins families
• evenness property of functions
• embedding theorems
• growth theorems
• Taylor series development of functions
• MSC2010: 32A30
• 30C45

The paper concerns complex-valued functions which are holomorphic in bounded complete n-circular domains and fulfil some geometric conditions. The families of such kind of functions were considered for instance by Bavrin [1,2], Dobrowolska and Liczberski [4], Dziubiski and Sitarski [5], Fukui [6], Higuchi [8], Jakubowski and Kamiski [9], Liczberski and Wrzesie [14], Marchlewska [15,16], Michiwaki [17], and Stankiewicz [22]. The above functions were applied later to research some families of locally biholomorphic mappings in (see for instance Pfaltzgraff and Suffridge [19], Liczberski [12], Hamada, Honda and Kohr [7]). In this paper, we consider an interesting family of the type which separates two Bavrin's families . These families correspond to the well-known families of convex univalent and close-to-convex univalent functions of one variable, respectively. We define using the property of evenness of functions. We obtain for some embedding theorems relevant to the mentioned separation question. Applying the Minkowski function of , we solve also some extremal problems for functions from . As an application, we give a topologic property of the family .

• 出版日期2014-6-3