等维Cartan-Hartogs域双全纯映射的特征

本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域Ω^Bm(μ)不是球,则它上面存在一函数X使得它在Ω^Bm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域Ω^Bm(μ)不是球,Ω^Bm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变.     

Reinhardt域上正规化双全纯凸映射的分解定理

研究了Cⁿ中Reinhardt域D_p = {(z₁, z₂, …, z_n)∈Cⁿ: 上正规化双全纯凸映射的结构问题, 给出了该类映射的分解定理. 作为特例, 证明了每个这样的映射f的第j个分量f_j (j= 1, 2, …, n), 展开式的前k项仅与z_j有关, 其中k是满足k＜min{ p¹ , p² , …, p_n}≤k + 1的自然数. 当p¹ , p² , …, p_n→∞时, 这将导出T. J. Suffridge关于多圆柱上凸映射类的分解定理.     

有界凸平衡域上的双全纯凸映照的判别准则

本文讨论Cn中有界强凸平衡域和凸平衡域上局部双全纯映照成为双全纯凸映照的充要条件,从而得到Reinhardt域Dp= 上双全纯凸映照的充要条件,其中Pj≥2(j=1,2,…,n).     

B_p~n上双全纯凸映照

本文给出了Suffridge结果的简单证明,并且构造出Reinhardt域B_p~n上的一些双全纯凸映照     

Bnp上双全纯凸映照

本文给出了Suffridge结果的简单证明,并且构造出Reinhardt域Bpn上的一些双全纯凸映照.     

B_p上双全纯凸映照

本文给出一个从B_p到C~n局部双全纯映照为双全纯凸映照的充要条件．     

有界对称域上的对角映射

文研究加权Bergman空间     

某类有界拟凸域双全纯不变量的极限

Ｅ＝Ｅ（ｍ，ｎ，ｋ）＝｛（ｚ，ω）∈Ｃ＾ｎ＋ｍ：│ｚ│＾２＋│ω│＾２ｋ〈１，ｚ∈Ｃ＾ｎ，ω∈Ｃ＾ｍ，ｋ〉０｝是Ｃ＾ｍ＋ｍ中的一类有界拟凸域。该文证明了在δＥ的强拟凸点上，当ｍ〉１时，ｌｉｍ（ｚ，ω）→δＥＪＥ（（ｚ，ω））＝π＾ｎ＋ｍ（ｎ＋ｍ＋１）＾ｎ／（ｎ＋ｍ）！．ｍ＝１时，ｌｉｎ（ｚ，ω）→δＥＪＥ（ｚ，ω））＝π＾ｎ＋１（ｎ＝）＾ｎ＋１／（ｎ＋１）！，在δＥ的弱拟凸点上，上述极限不存在。     

有界对称域上的对角映射

本文研究加权Ｂｅｒｇｍａｎ空间Ｌｐａ（Ωｎ,ｄμα）上的对角映射Ｄ,其中Ω是Ｃｍ中秩为ｒ,亏格为Ｎ的有界对称域．对Ωｎ上任何全纯函数Ｆ,证明了Ｆ∈Ｌｐａ（Ωｎ,ｄμα）当且仅当ＤＦ∈Ｌｐα（Ω,ｄλ｜α｜＋（ｎ－１）Ｎ）对于０＜Ｐ≤１和任意的权指标α＞－１成立,或者对于１＜ｐ＜∞和足够大的权指标α（与域Ω的秩有关）成立．     

Hilbert空间中的双全纯凸映照和双全纯星形映照的构造

利用复的Hilbert空间中的Riesz基{xj}及其对偶Riesz基{yj},引入新的算子Φ({xj},{yj},{gj})(z),来构造出复的Hilbert空间中的单位球β上的一些双全纯凸映照或双全纯星形映照,利用复的Hilbert 空间中的框架理论,得到此算子的一些性质,给出由复平面C中的单位圆△上的单叶凸函数或单叶星形函数,来构造复的Hilbert 空间X中的单位球β上的双全纯凸映照或双全纯星形映照的一些具体例子,同时也引入一些双全纯凸映照或双全纯星形映照的子类.     

Reinhardt域B_p上正规化双全纯完全准凸映射的齐次展式

本文主要研究C~n中有界凸Reinhardt域B_p上正规化双全纯完全准凸映射的齐次展开式问题,设f(z):B_p→C~n(p＞2)是一个正规化双全纯完全准凸映射,k是满足k＜p≤k+1的自然数,那么f_j(z)=z_j+α_(j2)z_j~2+…+α_(jk)z_j~k+O(|z|~(K+1)),其中f_j是f的第j个分量,j=1,2…．,n．     

有界星形域上的全纯映照成为星形映照的判别准则

本文讨论从有界星形圆形域和Carathedory完备域到Cn局部双全纯映照成为双全纯星形映照的充分必要条件．     

New Subclasses of Biholomorphic Mappings and the Modified Roper-Suffridge Operator

The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B~n in C~n is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ_(G,γ)(f)](z) preserves the properties of S_Ω~*(A, B), as well as strong and almost spirallikeness of type β and order α on B~n. Thus, the mappings in S_Ω~*(A, B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.     

Biholomorphic Mappings and the Extension Operators on New Hartogs Domains

In this paper, we generalize the Roper–Suffridge operator on the extended Hartogs domains.By using the geometric properties and the growth theorems of subclasses of biholomorphic mappings,we obtain the generalized operators preserve the properties of parabolic and spirallike mappings of type β and order ρ, S*_Ω(β, A, B), almost starlike mapping of complex order λ on ΩN under different conditions, and thus we get the corresponding results on the unit ball B~n in C~n. The conclusions lead to some known results.     

Linear Invariance of Locally Biholomorphic Mappings in Hilbert Spaces

We study the notion of linear invariance on the unit ball of a complex Hilbert space X and we obtain some connections between the norm-order of a linear invariant family (L.I.F.) and the quasi-convexity. Also, we give some results concerning the radius of univalence of some linear invariant families. Finally we find the norm-order of normalized convex mappings in the unit ball of X and some lower bounds for the radius of convexity and the radius of starlikeness for a certain L.I.F. in X .     

正规化双全纯映照的增长和掩盖定理

在一般复Banach空间的单位球上引入正规化全纯映照族Mg,考虑满足条件(Df(x))-f(x)∈M9的正规化局部双全纯映照f(其中x=0是f(x)-x的k+1阶零点)并得到其增长和掩盖定理.所得结果统一和推广了许多已知结论.     

关于局部双全纯映射的推广的Roper-Suffridge算子

§ 1.　Introduction　　LetUbetheunitdiskinCandBnbetheunitballinCn.In 1 995 ,RoperandSuffridgeintroducedanextensionoperator.ThisoperatorisdefinedforanormalizedlocallybiholomorphicfunctionfonUbyΦn(f) (z) =F(z) =(f(z1 ) ,f′(z1 )z′) ,z =(z1 ,z′)∈Bn,(1 .1 )wherez1 ∈U ,z′=(z2 ,… ,zn)∈Cn- 1 ,andthebranchofthesquarerootischosensuchthatf′(0 ) =1 .TheRoper Suffridgeextensionoperatorhasthefollowingimportantproperties:(a)IffisanormalizedconvexfunctiononU ,thenFisanormalizedconvexmappingon…     

Extension Operators Preserving Biholomorphic Mappings on Hartogs Domains*

In this paper, the authors extend the Roper-Suffridge operator on the generalized Hartogs domains. They mainly research the properties of the extended operator.By the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings, they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex order λ, almost spirallikeness of type β and order α, parabolic spirallikeness of type β and order ρ on the Hartogs domains in different co...