In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some r...In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.展开更多
A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommer...A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed.展开更多
In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.
In this paper, we establish distortion theorems for both normalized p-Bloch functions with branch points and normalized locally univalent p-Bloch functions defined on the unit disk, respectively. These distortion theo...In this paper, we establish distortion theorems for both normalized p-Bloch functions with branch points and normalized locally univalent p-Bloch functions defined on the unit disk, respectively. These distortion theorems give lower bounds on [f＇（z）] and sRf＇（z）. As applications of these distortion theorems, the lower bounds of the radius of the largest schlicht disk on these Bloch functions are given, respectively. Notice that when p= 1, our results reduce to that of Liu and Minda.展开更多
In this paper we establish characterizations of α-Bloch functions on the unit ball without use of derivative, which are stronger, more precise and general than those obtained by Nowak and Zhao.
In this paper we establish equivalent characterizations of α-Bloch functions on the unit ball without use of derivative, which generalize and improve the results of Nowak, Zhao, Wulan and Li.
Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. ...Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has展开更多
In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based o...In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based on the theorems.展开更多
Let f be analytic in a hyperbolic region Ω. The Bloch constant β_f of f is defined by β_f=sup z∈Ω|f’(z)|/λ_Ω(z), where λ_Ω(z)|dz|is the Poincare metric in Ω. Suppose △is hyperbolic and lim inf ω→cλ△(w...Let f be analytic in a hyperbolic region Ω. The Bloch constant β_f of f is defined by β_f=sup z∈Ω|f’(z)|/λ_Ω(z), where λ_Ω(z)|dz|is the Poincare metric in Ω. Suppose △is hyperbolic and lim inf ω→cλ△(w)】λ(△)】0, (?)c∈(?)△ where λ(△)=inf w∈△ λ△(w). Then for all f with f(Ω)(?)△, we have β_f≤1/λ(△). In this paper we study the extremal functions defined by β_f=1/λ(△) and the existence of those functions.展开更多
文摘In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.
基金This research was supported in part by a grant from the Vaisala Fund, Finland
文摘A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed.
文摘In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.
基金Supported by the National Natural Science Foundation of China(Grant No.11001246)Natural Science Foundation of Zhejiang Province(Nos.D7080080Y6090694)
文摘In this paper, we establish distortion theorems for both normalized p-Bloch functions with branch points and normalized locally univalent p-Bloch functions defined on the unit disk, respectively. These distortion theorems give lower bounds on [f＇（z）] and sRf＇（z）. As applications of these distortion theorems, the lower bounds of the radius of the largest schlicht disk on these Bloch functions are given, respectively. Notice that when p= 1, our results reduce to that of Liu and Minda.
基金the National Natural Science Foundation of China (Grant No. 10671093)
文摘In this paper we establish characterizations of α-Bloch functions on the unit ball without use of derivative, which are stronger, more precise and general than those obtained by Nowak and Zhao.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10871094 and 11071083）
文摘In this paper we establish equivalent characterizations of α-Bloch functions on the unit ball without use of derivative, which generalize and improve the results of Nowak, Zhao, Wulan and Li.
文摘Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has
基金The research is supported by NNSF of China(19771082)
文摘In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
文摘In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based on the theorems.
基金Supported by the National Natural Science Foundation of China.
文摘Let f be analytic in a hyperbolic region Ω. The Bloch constant β_f of f is defined by β_f=sup z∈Ω|f’(z)|/λ_Ω(z), where λ_Ω(z)|dz|is the Poincare metric in Ω. Suppose △is hyperbolic and lim inf ω→cλ△(w)】λ(△)】0, (?)c∈(?)△ where λ(△)=inf w∈△ λ△(w). Then for all f with f(Ω)(?)△, we have β_f≤1/λ(△). In this paper we study the extremal functions defined by β_f=1/λ(△) and the existence of those functions.
