In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatte...In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatten p-class（0〈p〈∞） Toeplitz operators on Dirichlet space D（Bn,dA） with unbounded symbols are also obtained.展开更多
In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class prop...In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class property criteria.On the eut-off c(N) we know that the phenomenon founded by Peloso is an exceptional case.展开更多
In this paper, we construct the function u in L2（Bn, dA） which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class （0 〈 p 〈 ∞） operator on pluriharmonic Bergman sp...In this paper, we construct the function u in L2（Bn, dA） which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class （0 〈 p 〈 ∞） operator on pluriharmonic Bergman space h2（Bn, dA） for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L1 symbols.展开更多
We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sutfficient conditions for such kind of weighted composition operators belo...We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sutfficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal Sp. As a corollary, we now have that Wφ,ψ is a Hilbert-Schmidt operator if and only if ∫Bn │ψ（w）│^2/（1-│φ（W）│^2）^n＋1 dV（W）〈∞展开更多
In this paper, we discuss the Schatten-p class （0 〈 p≤∞ ） of Toeplitz operators on generalized Foek space with the symbol in positive Borel measure. It makes a great difference from other papers by using the esti...In this paper, we discuss the Schatten-p class （0 〈 p≤∞ ） of Toeplitz operators on generalized Foek space with the symbol in positive Borel measure. It makes a great difference from other papers by using the estimates of the kernel and the weight together instead of separately estimating each other. We also get the equivalent conditions when a Toeplitz operator is in the Schatten-p class.展开更多
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 p...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.展开更多
文摘In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatten p-class（0〈p〈∞） Toeplitz operators on Dirichlet space D（Bn,dA） with unbounded symbols are also obtained.
文摘In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class property criteria.On the eut-off c(N) we know that the phenomenon founded by Peloso is an exceptional case.
基金Supported by National Natural Science Foundation of China(Grant No.11271092)
文摘In this paper, we construct the function u in L2（Bn, dA） which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class （0 〈 p 〈 ∞） operator on pluriharmonic Bergman space h2（Bn, dA） for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L1 symbols.
基金the National Natural Science Foundation of China(10471039)the Natural Science Foundation of the Education Commission of Jiangsu Province(03KJD140210,06KJD110175)the Natural Science Foundation of Xuzhou Institute of Technology(KY200508).
文摘We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sutfficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal Sp. As a corollary, we now have that Wφ,ψ is a Hilbert-Schmidt operator if and only if ∫Bn │ψ（w）│^2/（1-│φ（W）│^2）^n＋1 dV（W）〈∞
基金supported by NSFC(Grant Nos.11301101,11271092 and 11471084)the Guangzhou Higher Education Science and Technology Project(Grant No.2012A018)
文摘In this paper, we discuss the Schatten-p class （0 〈 p≤∞ ） of Toeplitz operators on generalized Foek space with the symbol in positive Borel measure. It makes a great difference from other papers by using the estimates of the kernel and the weight together instead of separately estimating each other. We also get the equivalent conditions when a Toeplitz operator is in the Schatten-p class.
文摘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.
