关于典型域到单位球上全纯映射的注记

给出了从典型域到单位球的全纯映射高阶Frchet导数的Schwarz-Pick估计,从而推广了单位球上全纯自映射Frchet导数的Schwarz-Pick估计以及单位圆盘上有界全纯函数高阶导数的Schwarz-Pick估计的结论.     

典型域上高阶Fréechet导数的Schwarz-Pick估计

本文给出了典型域上带正实部的全纯函数高阶Fr¶echet 导数的Schwarz-Pick 估计. 推广了单位圆盘和单位球上带正实部的全纯函数高阶偏导数的Schwarz-Pick 估计.     

SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.     

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on unit disk in C.     

A Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball

In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.     

Higher-Order Schwarz-Pick Estimates for Holomorphic Self-mappings on Classical Domains

In this paper,Schwarz-Pick estimates for high order Fréchet derivatives of holomorphic self-mappings on classical domains are presented.Moreover,the obtained result can deduce the early work on Schwarz...     

单位球上全纯函数的高阶Schwarz-Pick估计*

作者给出了单位球B_n ? Cⁿ到凸区域?? C上全纯函数的高阶Schwarz-Pick估计. 通过引入双曲度量,得到了单位圆盘D到凸区域?上全纯函数的系数估计. 应用该系数估计结果,得到单位球B_n到?内的全纯函数的高阶Schwarz-Pick估计.特别地, 当?是单位圆盘或右半平面时, 得到的结果分别与熟知的结果是一致的.     

A SCHWARZ-PICK LEMMA FOR THE MODULUS OF HOLOMORPHIC MAPPINGS FROM THE POLYDISK INTO THE UNIT BALL

In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.     

A Note on Schwarz-Pick Estimate

A Schwarz-Pick estimate of higher order derivative for holomorphic functions with positive real part on Bn is presented. This improves the earlier work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on the unit disk in C.     

The high order Schwarz-Pick lemma on complex Hilbert balls

In this paper we prove a high order Schwarz-Pick lemma for holomorphic mappings between unit balls in complex Hilbert spaces. In addition, a Schwarz-Pick estimate for high order Fréchet derivatives of a holomorphic function f of a Hilbert ball into the right half-plane is obtained.     

Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广

对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计.     

Schwarz-Pick estimates for bounded holomorphic functions in the unit ball of ℂ n

We give a Schwarz-Pick estimate for bounded holomorphic functions on unit ball in Cn, and generalize some early work of Schwarz-Pick estimates for bounded holomorphic functions on unit disk in C.     

Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.     

Another look at the Burns-Krantz theorem

We obtain a generalization of the Burns-Krantz rigidity theorem for holomorphic self-mappings of the unit disk in the spirit of the classical Schwarz-Pick Lemma and its continuous version due to L. Harris via the generation theory for one-parameter semigroups. In particular, we establish geometric and analytic criteria for a holomorphic function on the disk with a boundary null point to be a generator of a semigroup of linear fractional transformations in term of relations among three boundary derivatives of the function at this point.     

SCHWARZ-PICK ESTIMATES FOR PARTIAL DERIVATIVES OF ARBITARY ORDER OF BOUNDED HOLOMORPHIC FUNCTIONS IN THE UNIT BALL OF C~n

This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of C n .     

The Julia-Wolff-Carathéodory theorem in polydisks

The classical Julia-Wolff-Carathéodory theorem gives a condition ensuring the existence of the non-tangential limit of both a bounded holomorphic function and its derivative at a given boundary point of the unit disk in the complex plane. This theorem has been generalized by Rudin to holomorphic maps between unit balls inC ⁿ and by the author to holomorphic maps between strongly (pseudo)convex domains. Here we describe Julia-Wolff-Carathéodory theorems for holomorphic maps defined in a polydisk and with image either in the unit disk, or in another polydisk, or in a strongly convex domain. One of the main tools for the proof is a general version of the Lindelöf principle valid for not necessarily bounded holomorphic functions.     

Generalization of theorems of Szász and Ruscheweyh on exact bounds for derivatives of analytic functions

Let Ω and Π be two domains in the extended complex plane equipped by the Poincaré metric. In this paper we obtain analogs of Schwarz-Pick type inequalities in the class A(Ω, gH) = {f: Ω → Π} of functions locally holomorphic in Ω; for the domain Ω we consider the exterior of the unit disk and the upper half-plane. The obtained results generalize the well-known theorems of Szász and Ruscheweyh about the exact estimates of derivatives of analytic functions defined on the disk |z| < 1.     

The Generalized Schwarz–Pick Estimates of Arbitrary Order on the Unit Polydisk

Let Ω be a homogeneous circular convex domain (a bounded symmetric domain) in ${\mathbb{C}^N}$ containing the origin. The generalization of the Schwarz–Pick estimates of partial derivatives of arbitrary order are established for holomorphic mappings from the unit polydisk D _n to Ω associated with the Carathéodory metric. The metric enables us to obtain some known results from a unified perspective and also leads some new results. In particular, our results are valid for the Cartan domains. When Ω = B _N , the Schwarz–Pick estimates of high order reduces to that of Liu and Chen.     

多复变数全纯映射精细的Bohr定理

本文首先建立不依赖自同构从复Banach空间平衡域到Cn单位多圆柱上一定限制条件下全纯映射精细的范数型Bohr定理及复Banach空间X上单位球到复Banach空间Y上单位球全纯映射精细的泛函型Bohr定理.其次,给出有界对称域上全纯映射精细的Bohr定理.最后,得到J*代数单位球上全纯映射精细的Bohr定理.所得结果将一维的Bohr定理推广至高维.     

Fekete and Szeg problem in one and higher dimensions

In this paper, we establish the Fekete and Szeg inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C~n.