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 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 .     

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 Pointwise Multipliers From Space F（p, q, s） to Bloch Type Space in C^n

Let B be the unit ball in C^n. By H(B) we denote the class of all holomorphic functions on B and H^∞ denotes the class of all bounded holomorphic functions on B.     

The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables

In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions■are given,where k is a positive integer,and G is a balanced domain in complex Banach spaces.In particular,the results of first order Fréchet derivative for the above functions and higher order Frechet derivatives for positive real part holomorphic functions■are sharp for G=B,where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces.Their results reduce to the classic...     

单位球加权伯格曼空间上托普里兹算子的乘积

We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We furthermore obtain necessary and sufficient conditions for bounded Haplitz products HfTg-,where f∈L2(Bn,dvα) and g is a square integrable holomorphic function.     

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.     

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.     

The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variables

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in ■~n,which are natural extensions to higher dimensions of some Fekete and Szeg? inequalities for subclasses of the normalized univalent functions in the unit disk.     

The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variable

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in ■ⁿ,which are natural extensions to higher dimensions of some Fekete and Szeg? inequalities for subclasses of the normalized univalent functions in the unit disk.     

POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS

We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.     

解析簇上Leray-Stokes型积分表示公式（英文）

The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C~n, firstly using different method and technique we derive the corresponding integral representation formulas of differentiable functions for complex n-m(0 ≤ m n) dimensional analytic varieties in the two types of the bounded domains. Secondly we obtain the unified integral representation formulas of differentiable functions for complex n-m(0 ≤ m n) dimensional analytic varieties in the general bounded domains. When functions are holomorphic, the integral formulas in this paper include formulas of Stout~([1]), Hatziafratis~([2]) and the author~([3]),and are the extension of all the integral representations for holomorphic functions in the existing papers to analytic varieties. In particular, when m = 0, firstly we gave the integral representation formulas of differentiable functions for the two types of bounded domains in C~n. Therefore they can make the concretion of Leray-Stokes formula. Secondly we obtain the unified integral representation formulas of differentiable functions for general bounded domains in C~n. So they can make the Leray-Stokes formula generalizations.     

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.     

Bloch型空间之间的广义Cesaàro算子

We characterize the symbol ψ for which the induced extended Cesaro operator Tψ: Bω→Bμ, (respectively,Bω,0→Bμ,0) is bounded or compact, where ψ is a given holomorphic function on the unit disc D,ω and μ both are normal functions on [0,1).     

AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.     

SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS IN COMPLEX CLIFFORD ANALYSIS

In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cn+1, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△mf=0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cn+1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.     

UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n

Abstract In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.     

COMPACT COMPOSITION OPERATORS ON GENERALIZED LIPSCHITZ SPACES

In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces Λα (α > 1) of holomorphic functions in the unit disk are characterized.     

The Pointwise Multipliers From Space F(p, g, s) to Bloch Type Space in Cn

1 IntroductionLet B be the unit ball in Cn. By H(B) we denote the class of all holomorphic functions on B and H∞ denotes the class of all bounded holomorphic functions on B .For α ∈ B , let g(z,α) = log |ψα(z)|-1 be Green's function for B with logarithmic singularity at a, where ψα is the Mobius transformation of B satisfying ψα(0) =α,ψα(α) =0, ψα = ψα-1.Difinition 1 Let 0 < p. s < ∞, -n - 1 < q < ∞. We say f ∈ F(p, q, s) provided that     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.