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
用T_k表示在单位圆E={z:∣z∣<1}内解析,形如f(z)=z-α_2z^2-α_3z^3-……-α_nz^n-……(α_n≥0,n≥2)的函数之全体。对于T_k的子类L_k(α,β,γ),将证明如果f∈L_k(α,β,γ),那么函数F_c(f)=(c+1)/z^c integral from 0 to Z t^(c-...用T_k表示在单位圆E={z:∣z∣<1}内解析,形如f(z)=z-α_2z^2-α_3z^3-……-α_nz^n-……(α_n≥0,n≥2)的函数之全体。对于T_k的子类L_k(α,β,γ),将证明如果f∈L_k(α,β,γ),那么函数F_c(f)=(c+1)/z^c integral from 0 to Z t^(c-1)f(t)dt也属于L_k(α,β,γ)。展开更多
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.
文摘用T_k表示在单位圆E={z:∣z∣<1}内解析,形如f(z)=z-α_2z^2-α_3z^3-……-α_nz^n-……(α_n≥0,n≥2)的函数之全体。对于T_k的子类L_k(α,β,γ),将证明如果f∈L_k(α,β,γ),那么函数F_c(f)=(c+1)/z^c integral from 0 to Z t^(c-1)f(t)dt也属于L_k(α,β,γ)。
