THE EQUIVALENT CHARACTERIZATION OF F(p,q,s)SPACE ON BOUNDED SYMMETRIC DOMAINS OF Cn

LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.

Weighted Bergman Spaces on Bounded Symmetric Domains

On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.

Compactness of Composition Operators from the p-Bloch Space to the q-Bloch Space on the Classical Bounded Symmetric Domains

In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.

Coefficient multipliers of H^p spaces over bounded symmetric domains in C

One way to give information about the Taylor coefficients of Hp functions is to describe the multipliers of Hp into various spaces. In the case of one complex variable, Duren and Shields described the multipliers of Hp into lq (0<p<1, p≤q≤∞). The Duren-Shields theorems to the case with the bounded symmetric domains in Cn are generalized. The results are sharp if q≥2. A sufficient condition of Hp into Hq is given for any p and q, 0<p<q<∞.

On the Multipliers of H^p Spaces on Bounded Symmetric Domains

Let Ω be a bounded symmetric domain in Cn which contains the origin, b its Silov boundary and Γ its holomorphic automorphism group. Let Γ0 be a subgroup of F with fixed point origin. There exists a unique Γ0-invariant measure σ on b such that σ（b）=1. We denote the unit ball in Cn by B and the unit disc in C by U.

D^p Spaces on Bounded Symmetric Domains of C^n

In this paper,the space D^p(Ω)of functions holomorphic on bounded symmetric domain of C^n is defined.We prove that H^P(Ω) D^P(Ω)if 0【p≤2 and D^P(Ω) H^P(Ω)if p≥2,and both the inclusions axe proper.Further,we find that some theorems on H^p(Ω)can be extended to a wider class D^P(Ω)for 0【p≤2.

Bloch spaces on bounded symmetric domains in complex Banach spaces

We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.

H^p Multipliers on Bounded Symmetric Domains

The following results are obtained in this paper: (i) if and then is a multiplier of into then thereis a sequence with which is not a multiplier of Hp(B) intothen there is a sequence with which is not a muitiplier of HP(B) into Hq(B).

Automorphism groups of causal symmetric spaces of Cayley type and bounded symmetric domains

Symmetric spaces of Cayley type are a higher dimensional analogue of a onesheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D.

Pluriharmonic Functions on Bounded Symmetric Domains of C^n

1 Introduction Let Ω be a bounded symmetric domain in the complex vector space Cn, 0∈Ω, with Bergman-Silov boundary b, Γ the group of holomorphic automorphisms of Ω and Γ0 its isotropy group. It is known that Ω is circular and star-shaped with respect to 0 and that b is circular. The group Γ0 is transitive on b and b has a unique normalized Γ0-invariant measure σ with σ（b）= 1. Hua constructed by group representation theory a system {φkv}

Jackson's Theorem on Bounded Symmetric Domains

Polynomial approximation is studied on bounded symmetric domain Ω in C^n for holomorphic function spaces X such as Bloch-type spaces, Bergman-type spaces, Hardy spaces, Ω algebra and Lipschitz space. We extend the classical Jackson＇s theorem to several complex variables：Eκ（f,X）≤ω（1/k,f,X）, where Eκ（f,X） is the deviation of the best approximation of f ∈X by polynomials of degree at most k with respect to the X-metric and ω（1/k,f,X） is the corresponding modulus of continuity.

Composition Operators on Weighted Bergman Spaces of Bounded Symmetric Domains

The purpose of this paper is to study the composition operators on weightedBergman spaces of bounded symmetric domains.The sufficient and necessary conditions for a composition operator C"to be bounded add corn pact respectively are given in term of the concept of Carleson measure.Meanwhile,the integral characteristic of n such that Cn is a Schatten p-class operator is obtained.

有界对称域上A^p空间的一些性质

讨论了Cn 中有界对称域Ω上Bergman空间Ap 中函数的系数性质 ,并利用这些结果给出了有界对称域上Ap 空间到lq 及l∞ 的几个乘子定理 .

A^p空间系数乘子的性质

乘子理论已经有一个很长的历史,Hardy-Littlewood结论对复分析三个经典问题用乘子语言做了解释。因此它是一个非常有趣而重要的研究领域。该文讨论了在Cn中Bergman空间中函数的系数乘子,推广了单复变Ap的性质,并将结果推广到有界对称域上,给出了有界对称域上Ap到Aq的乘子定理,还得到了Ap到Bloch空间的乘子定理。

有界对称域上混合范数空间A^(p,q,α)的一些性质

该文讨论了在Cn中的有界对称域上混合范数空间Ap,q,α中的函数与其Fourier展开式的关系,推广了单复变混合范数空间Ap,q,α空间的性质,给出了有界对称域上Ap,q,α到l∞的乘子定理。

有界对称域上Bergman空间A^p的乘子定理

有界对称域上Hp(Ω)到lq(0<q≤∞)的乘子定理已被证明.在此基础上,应用乘子语言来刻画全纯函数的Taylor系数的方法,得到了有界对称域上Ap(Ω)到lq(0<q≤∞)的乘子定理的充分条件,并得到了在单位球上的必要条件.

oeplitz算子和Hankel算子之紧性研究

给出ｎ中有界对称区域的Ｂｅｒｇｍａｎ空间上具有Ｌ∞—符号中的Ｔｏｅｐｌｉｔｚ算子和Ｈａｎｋｅｌ算子为紧算子的充要条件。最后还得到一些推论。

有界对称域上的D^p乘子

设Ω是n中包含原点的有界对称域．本文就Ω上的Dp空间得到了两个乘子定理．

A^2(Ω,dV_α)空间上Schatten类复合算子

让Ａ２（Ω，ｄＶα）表示Ｌ２（Ω，ｄＶα）中的解析函数的全体，它是Ｌ２（Ω，ｄＶα）的闭子空间．本文研究了Ａ２（Ω，ｄＶα）上的具有符号ｂ的复合算子Ｃｂ．得到了这种复合算子属于Ｓｃｈａｔｔｅｎ－Ｖｏｎ Ｎｅｕｍａｎｎ理想Ｓｐ的几个充要条件．

多复变数Bergman空间中的Hardy-Littlewood定理

在■~n叫,有界对称域上的Bergman 空间中建立了Hardy-Littlewood 定理,并用更一般的分数次导数D~βf(β≥0)替代了单复变中的通常导数f'.最后还将这一结果推广到了更一般的解析函数空间中.