关于α次的β型螺形映照推广的Roper-Suffridge算子

对Cn中某一Reinhardt域上以及复Hilbert空间单位球上推广的Roper-Suffridge算子保持α(0《α《1)次的β(-π/2《β《π/2)型螺形性进行了讨论.所得的结果推广了以前相应的结论.     

ε星形映照族(Ⅰ)

本文定义了ε星形映照族,用统一的观点来处理复Banach空间、Cn及C中的各种区域上的凸映照族与星形映照族,研究它们之间是如何过渡的,并讨论了其判别准则及Roper-Suffridge算子.     

典型域上R—W多项式及内函数的存在性

该文给出了多复变四类典型域（m，n）,（n）,(2k),（3）及(n)上的R－W型多项式,并证明了这些区域上内函数的存在性．     

On growth and covering theorems of quasi-convex mappings in the unit ball of a complex banach space

A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space is confined to ℂⁿ, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge.     

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.     

C^n中Lie球RIV（n）上的偏差定理 献给钟同德教授八十华诞

本文引入了Lie球双曲空间上映照族Hm（RIV（n））,满足m阶Jacobi行列式为零的全纯映照子族．而且当m趋于无穷时,该映照族就是RIV（n）上的局部双全纯映照族．作者用分析的方法给出了Hm（RIV（n））上的偏差定理．当m=1和m→＋∞时,结果分别都回到了Gong关于Lie球RIV（n）上的偏差定理;当n=1,其结果又回到了Liu和Minda在单位圆盘上的偏差定理．本文的方法也不同于以前．作为偏差定理的一个应用,给出了不同映照族Hm（RIV（n））上的Bloch常数估计．