单位球上加权Bergman空间上加权复合算子的本性范数

本文给出了单位球上加权Bergman空间上的加权复合算子的本性范数,并刻画了这类加权复合算子的有界性和紧性.     

加权Bergman空间上的Carleson测度与Toeplitz算子

探讨加权Bergman空间Ap()上的Carleson型测度和具有非负测度符号的Toeplitz算子,给出Carleson测度或消没Carleson测度的若干等价描述并用Carleson测度的方法刻画了Toeplitz算子是有界的或紧致的充要条件.     

Riemann-Stieltjes Operators on Weighted Bloch and Bergman Spaces of the Unit Ball

Riemann–Stieltjes integrals are considered as linear operatorson weighted Bloch and Bergman spaces of the open unit ball inseveral complex variables. For weighted Bloch spaces, boundedness,compactness and weak compactness of Riemann–Stieltjesoperators are characterized by means of certain growth propertiesof holomorphic symbols. For weighted Bergman spaces, some criteriaare given for Riemann–Stieltjes operators with holomorphicsymbols to be bounded, compact and of Schatten–von Neumann'sideal.     

加权Begman空间的加权复合算子的本性模

利用上极限,给出了单位球上加权Bergman空间的加权复合算子的本性模的表示．     

Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees

Hastings studied Carleson measures for non-negative subharmonic functions on the polydisk and characterized them by a certain geometric condition relative to Lebesgue measure σ. Cima & Wogen and Luecking proved analogous results for weighted Bergman spaces on the unit ball and other open subsets of \(\mathbb {C}^{n}\). We consider a similar problem on a homogeneous tree, and study how the characterization and properties of Carleson measures for various function spaces depend on the choice of reference measure σ.     

Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball

We study the so-called radial operators, and in particular radial Toeplitz operators, acting on the standard weighted Bergman space on the unit ball in ${\mathbb{C}^n}$ . They turn out to be diagonal with respect to the standard monomial basis, and the elements of their eigenvalue sequences depend only on the length of multi-indexes enumerating basis elements. We explicitly characterize the eigenvalue sequences of radial Toeplitz operators by giving a solution for the weighted extension of the classical Hausdorff moment problem, and show that the norm closure of the set of all radial Toeplitz operators with bounded measurable radial symbols coincides with the C*-algebra generated by these Toeplitz operators and is isomorphic and isometric to the C*-algebra of sequences that slowly oscillate in the sense of Schmidt.     

加权调和Bergman核及其诱导的度量矩阵

在Rn中的有界域上建立加权调和Bergman核,并得出单位球的加权调和Bergman核的表达式;利用加权调和Bergman核在Rn的有界域上构造度量矩阵;得到关于调和映射的Jacobi矩阵与度量矩阵之间的一个不等式.     

Carleson Measures for Besov-Sobolev Spaces with Applications in the Unit Ball of C

This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces B_p^σ (B) and p-Carleson measure in the unit ball of Cⁿ. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on B_p^σ (B) spaces by means of Carleson measures for B_p^σ (B).     

Essential Norm Estimates for Little Hankel Operators on Weighted Bergman Spaces of the Unit Ball

We give estimates for the essential norm of a bounded little Hankel operator with $L^2$ symbol on weighted Bergman spaces of the unit ball in terms of a certain integral transform of the symbol. As an application of these estimates, we also give a necessary and sufficient condition for the little Hankel operators to be compact.     

Cn中单位球上几个全纯函数空间上加权复合算子的有界性

讨论了C^n上单位球中p-Bloch空间上加权复合算子Tφ，ψ的有界性，得到Tφ，ψ是β′到β′有界算子的几个充分条件，此外还讨论了p-Bloch空间和小p-Bloch空间上复合算子T1，ψ的有界性，得到了几个充分条件和必要条件，就单位球的情形扩展了[2]的结论．     

Cn中有界对称域上不同加权Bergman空间之间的复合算子

本文研究了Cn中有界对称域Ω上不同加权Bergman空间之间的复合算子,引入了η-αCarleson测度,利用它作为工具给出了有界的或紧的复合算子Cφ:Lαp(Ω,dνα)Lαq(Ω,dνβ)的特征.     

单位球加权Bergman空间上的乘法算子

函数空间上的乘法算子是包含许多重要算子的算子类,本文主要研究了单位球加权Bergman空间上乘法算子的性质.     

Cn中单位球上的Dirichlet空间和Qp,0空间

In this paper, we first give some new characterizations of Qp,0 spaces by means of vanishing p-Carleson measure. Using these results, we can prove that Dirichlet space is a subset of Qp,0 for(n-1)/n相似文献   

Little Hankel Operators on the Weighted Bergman Space of the Unit Ball

In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.     

单位球上Hardy空间之间的加权复合算子

We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H1 to H1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.     

单位球上Bergman空间到Besov空间的广义Cesaro算子(英文)

本文利用Carleson测度刻画了Bergman空间到Besov空间的广义Cesaro算子T_g的有界性和紧性,同时得到了(p,q)-φCarleson测度的一些性质.     

Cn中单位球上一些全纯函数空间的特征

对p＞0,-∞＜s＜∞,Cn中的球B上的Bergman空间Lpa(B)等同于B上满足的全纯函数f的全体当且仅当s＞max{0,2-p}.此处和λ分别是B上的不变梯度和不变测度.对B上的Bloch函数空间,也有着相应的特征刻划.作为这些结果的应用,本文解决了欧阳才衡、杨徽生和赵如汉的一个猜测.     

Bounded and Invertible Toeplitz Products on Vector Weighted Bergman Spaces of the Unit Polydisc

We characterize bounded and invertible Toeplitz products on vector weighted Bergman spaces of the unit polydisc. For our purpose, we will need the notion of Békollé–Bonami weights in several parameters.