单位圆内代数体函数的T半径

应用Ahlfors覆盖曲面的方法,在单位圆内构造了代数体函数的一个新的奇异半径(称为T半径),并应用无穷级的型函数推广了亚纯函数奇异方向的相关结论.     

拟亚纯映射的Borel点

对于平面上的Ｋ拟亚纯映射,利用孙道椿,杨乐［１］建立的一个基本不等式,讨论了拟亚纯映射在单位圆内的奇异Ｂｏｒｅｌ点．将亚纯函数的有关结果［２］推广到Ｋ拟亚纯映射．     

圆内亚纯函数充满圆及其应用

<正> 复平面内的充满圆序列在值分布论中有许多重要应用.对圆内亚纯函数的充满圆序列却比较复杂,相当困难.虽有人研究但总是不理想,不便应用.本文首先定义了圆内的充满圆序列,并证明 Borel 点附近存在充满圆序列,从而得到有穷正级圆内亚纯函数存在充满圆序列.最后作为应用证明了对应于 Hayman 不等式的奇异点存在.     

单位圆内亚纯函数的奇异点

本文对单位圆内零级亚纯函数得到了一个较为广泛的与正规定则相应的奇异点的存在性,并由此得到如下结果：若单位圆|z|＜1内的亚纯函数满足则存在点eiθ0（≤θ0＜2π）使得对任意正数ε＞0任意正整数。n≥1,恒有limr→l-0n（r,θ0,ε;flfm=a）=＋∞对每一有穷非零复数a成立．     

单位圆内拟亚纯映射的重值

单位圆内充满圆序列是一个复杂的问题,该文改进了现有一些证法,使单位圆内充满圆证法类似于平面上充满圆证法.同时得到单位圆内K-拟亚纯映射涉及重值的充满圆序列及相应的奇异半径     

单位圆内亚纯函数的充满圆

本文推广了Ahlfors不等式，给出了亚纯函数的充满圆的一个几何特征，从而证明了单位圆内亚纯函数的充满圆序列的存在性.此外还举例说明了这些结果就充满圆的指数而言是最好的．     

单位圆内拟亚纯映射的奇异点

本文通过一般化Tsuji的一个结果,证明了单位圆内零级K-拟亚纯映射涉及重值的一类奇异点的存在性.     

单位圆内允许亚纯函数的唯一性

研究单位圆内允许亚纯函数的唯一性 ,得到了一系列的结果 .     

单位圆内拟亚纯映射的最大型Borel点的存在性及其性质

该文先证明了单位圆内K-拟亚纯映射关于角域内的一个基本不等式,并应用此不等式讨论了单位圆内有穷级K-拟亚纯映射的最大型Borel点的存在及其性质.     

单位圆内亚纯函数的奇异方向

本文研究了单位圆内亚纯函数的一种新奇异方向，并由此得出了另外两个重要结论。     

THE SECTIONS OF ODD UNIVALENT FUNCTIONS

Let $\[{S_k}\]$ be the class of functions $\[f(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}} \]$ which are regular and univalent in $\[\left| z \right| < 1\]$ and denote $\[S_n^{(k)}(z) = z + \sum\limits_{m = 1}^\infty {b_{mk + 1}^{(k)}{z^{mk + 1}}} \]$. The authors prove that the functions $\[S_n^{(2)}(z)\]$ are starlike in $\[\left| z \right| < \frac{1}{{\sqrt 3 }}\]$.     

Convex Holes Produce Lower Bounds for Coefficients

Let D denote the open unit disk and $ f:D \to \bar {{\bf C}}$ be meromorphic and injective in D . Especially, we consider such f which have an expansion $$ f(z) = z + \sum \limits_{n=2}^{\infty }a_n(\;f\,)z^n $$ in a neighbourhood of the origin and map D onto a domain whose complement with respect to $\bar {{\bf C}}$ is convex. Let the set of these functions be denoted by Co . We fix | f m 1 ( X )| for f ] Co and determine the inner and outer radius of the ring domain which is the domain of variability of a 2 ( f ) for such f . Further, it is shown that f ] Co implies that $$ \phi (z) = z+2 {f'(z) \over f''(z)}$$ is holomorphic in D and maps D into itself. This implication in turn implies the inequalities | a n ( f )| S 1 for f ] Co and n = 2,3,4. In addition, we show that | a n ( f )| S 1/2 for f ] Co and all n S 2 .     

Cn中单位球上$mu$-Bloch函数的等价刻画

设$\mu$是$[0,1)$上的正规函数, 给出了${\bf C}^{\it n}$中单位球$B$上$\mu$-Bloch空间$\beta_{\mu}$中函数的几种刻画. 证明了下列条件是等价的: (1) $f\in \beta_{\mu}$; \ (2) $f\in H(B)$且函数$\mu(|z|)(1-|z|^{2})^{\gamma-1}R^{\alpha,\gamma}f(z)$ 在$B$上有界; (3) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{1}-1}\frac{\partial^{M_{1}} f}{\partial z^{m}}(z)}$ 在$B$上有界, 其中$|m|=M_{1}$; (4) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{2}-1}R^{(M_{2})}f(z)}$ 在$B$上有界.     

由卷积和从属关系刻画的单叶调和函数某些子类

Let SH be the class of functions f = h + ˉg that are harmonic univalent and sensepreserving in the open unit disk U = {z ∈ C : |z| 1} for which f(0) = f′(0)-1 = 0. In the present paper, we introduce some new subclasses of SH consisting of univalent and sensepreserving functions defined by convolution and subordination. Sufficient coefficient conditions,distortion bounds, extreme points and convolution properties for functions of these classes are obtained. Also, we discuss the radii of starlikeness and convexity.     

Interpolating and sampling sequences for entire functions

We characterise interpolating and sampling sequences for the spaces of entire functions f such that $ f e^{-\phi}\in L^p(\C)$, $p\geq 1 $, where $\phi$ is a subharmonic weight whose Laplacian is a doubling measure. The results are expressed in terms of some densities adapted to the metric induced by $\Delta\phi$. They generalise previous results by Seip for the case $\phi(z)=|z|^2$, Berndtsson and Ortega-Cerdà and Ortega-Cerdà and Seip for the case when $\Delta\phi$ is bounded above and below, and Lyubarskiĭ and Seip for 1-homogeneous weights of the form $\phi(z)=|z|h(\arg z)$, where h is a trigonometrically strictly convex function.     

关于p-叶星形性和强星形性的充分条件 (英)

本文利用微分从属的方法得到了单位圆盘内p-叶星形函数和强星形函数的某些充分条件．     

ESTIMATE OF d_0/d~* FOR STARLIKE FUNCTIONS

Let S~* be the class of functionsf(z)analytic,univalent in the unit disk|z|<1 andmap|z|<1 onto a region which is starlike with respect to w=0 and is denoted as D_f.Letr_0=r_0(f)be the radius of convexity of f(2).In this note,the author proves the following result:(d_0/d~*)≥0.4101492,where d_0= f(z),d~*=|β|.     

Characterization and the pre-Schwarzian norm estimate for concave univalent functions

Let Co(α) denote the class of concave univalent functions in the unit disk ${\mathbb{D}}$ . Each function ${f\in Co(\alpha)}$ maps the unit disk ${\mathbb{D}}$ onto the complement of an unbounded convex set. In this paper we find the exact disk of variability for the functional ${(1-|z|^2)\left ( f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ . In particular, this gives sharp upper and lower estimates for the pre-Schwarzian norm of concave univalent functions. Next we obtain the set of variability of the functional ${(1-|z|^2)\left(f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ whenever f′′(0) is fixed. We also give a characterization for concave functions in terms of Hadamard convolution. In addition to sharp coefficient inequalities, we prove that functions in Co(α) belong to the H ^p space for p < 1/α.     

与分担全纯函数相关的正规族

设F是在区域D内的一族亚纯函数,其零点重级至少为k,k是一个正整数,a(z)(≠0)在区域D内全纯.若对于任意的f∈F,有(1)f(z)与a(z)没有公共的零点;(2)f(z)=0f(k)(z)=a(z)■0|f~((k+1))(z)-a'(x)||a(z)|,则F在D内正规.     

典型實照函數的最小?妥钚∑

<正> 1.如果函數f(z)在包含實軸土某一區間的區域B中是正則的,f(z)在此實軸區間上取實值.在區域B的其餘地方f(z)與(z)同符號;即