A new inclusion for Bavrin's families of holomorphic functions in n-circular domains
The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete -circular domains and fulfil some geometric conditions. Such families were applied later to research some families of locally biholomorphic mappings in . (see for instance, J. A....
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| Veröffentlicht in: | Mathematica Slovaca Jg. 66; H. 4; S. 845 - 852 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.08.2016
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| ISSN: | 0139-9918, 1337-2211 |
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| Abstract | The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete
-circular domains
and fulfil some geometric conditions. Such families
were applied later to research some families of locally biholomorphic mappings in
. (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families
were obtained by [BAVRIN, I. I.:
, Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DŁUGOSZ, R.:
, J. Appl. Anal.
(2013), 153--165], [DŁ UGOSZ, R.—LEŚ, E.:
, Complex Var. Elliptic Equ.
(2014), 883--899], [LEŚ-BOMBA, E.—LICZBERSKI, P.:
, Demonstratio Math.
(2009), 491--503], et al.. |
|---|---|
| AbstractList | The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete
-circular domains
and fulfil some geometric conditions. Such families
were applied later to research some families of locally biholomorphic mappings in
. (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families
were obtained by [BAVRIN, I. I.:
, Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DŁUGOSZ, R.:
, J. Appl. Anal.
(2013), 153--165], [DŁ UGOSZ, R.—LEŚ, E.:
, Complex Var. Elliptic Equ.
(2014), 883--899], [LEŚ-BOMBA, E.—LICZBERSKI, P.:
, Demonstratio Math.
(2009), 491--503], et al.. The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete n -circular domains G ⊂ C n $\mathcal{G} \subset \mathbb{C}^{n}$ and fulfil some geometric conditions. Such families X G $\mathcal{X}_{G}$ were applied later to research some families of locally biholomorphic mappings in C n $\mathbb{C}^{n}$ . (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families X G $\mathcal{X}_{G}$ were obtained by [BAVRIN, I. I.: A Class of Regular Bounded Functions in the Case of Several Complex Variables and Extreme Problems in That Class , Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DŁUGOSZ, R.: Embedding theorems for holomorphic functions of several complex variables , J. Appl. Anal. 19 (2013), 153--165], [DŁ UGOSZ, R.—LEŚ, E.: Embedding theorems and extremal problems for holomorphic functions on circular domains of C n $\mathbb{C}^{n}$ , Complex Var. Elliptic Equ. 59 (2014), 883--899], [LEŚ-BOMBA, E.—LICZBERSKI, P.: New properties of some families of holomorphic functions of several complex variables , Demonstratio Math. 42 (2009), 491--503], et al.. The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete [n]-circular domains G⊂Cn$\mathcal{G} \subset \mathbb{C}^{n}$ and fulfil some geometric conditions. Such families XG$\mathcal{X}_{G}$ were applied later to research some families of locally biholomorphic mappings in Cn$\mathbb{C}^{n}$. (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families XG$\mathcal{X}_{G}$ were obtained by [BAVRIN, I. I.: [A Class of Regular Bounded Functions in the Case of Several Complex Variables and Extreme Problems in That Class], Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DLUGOSZ, R.: [Embedding theorems for holomorphic functions of several complex variables], J. Appl. Anal. 19 (2013), 153--165], [DL UGOSZ, R.--LES, E.: [Embedding theorems and extremal problems for holomorphic functions on circular domains of]Cn$\mathbb{C}^{n}$, Complex Var. Elliptic Equ. 59 (2014), 883--899], [LES-BOMBA, E.--LICZBERSKI, P.: [New properties of some families of holomorphic functions of several complex variables], Demonstratio Math. 42 (2009), 491--503], et al.. The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete [n]-circular domains G⊂ Cn$\mathcal{G} \subset \mathbb{C}n}$ and fulfil some geometric conditions. Such families XG$\mathcal{X}_{G}$ were applied later to research some families of locally biholomorphic mappings in Cn$\mathbb{C}n}$. (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families XG$\mathcal{X}_{G}$ were obtained by [BAVRIN, I. I.: [A Class of Regular Bounded Functions in the Case of Several Complex Variables and Extreme Problems in That Class], Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DLUGOSZ, R.: [Embedding theorems for holomorphic functions of several complex variables], J. Appl. Anal. 19 (2013), 153--165], [DL UGOSZ, R.--LES, E.: [Embedding theorems and extremal problems for holomorphic functions on circular domains of]Cn$\mathbb{C}n}$, Complex Var. Elliptic Equ. 59 (2014), 883--899], [LES-BOMBA, E.--LICZBERSKI, P.: [New properties of some families of holomorphic functions of several complex variables], Demonstratio Math. 42 (2009), 491--503], et al.. |
| Author | Sibelska, Agnieszka Długosz, Renata Leś, Edyta |
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| Snippet | The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete
-circular domains
and fulfil some... The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete n -circular domains G ⊂ C n... The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete [n]-circular domains G⊂Cn$\mathcal{G}... The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete [n]-circular domains G⊂ Cn$\mathcal{G}... |
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| SubjectTerms | 30C45 Circularity Complex variables Extreme values Functions (mathematics) holomorphic functions of several complex variables Inclusions Mapping Mathematical analysis n-circular domains Primary 32A30 starlike and convex functions the Minkowski function the Temljakov operator Theorems |
| Title | A new inclusion for Bavrin's families of holomorphic functions in n-circular domains |
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