Fock-Sobolev空间上有界、紧与S_p-类算子

本文研究Fock-Sobolev空间上稠密定义算子,将这些算子统一表示成积分算子,利用积分算子的方法得到了它们的一个充分条件,并构造反例说此充分条件是非必要的,还得到这些算子为紧算子的两个充分条件.最后构造符号函数在复平面上每一点处本性无界的紧和Sp-类(0p∞)Toeplitz算子.     

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p   class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range 0<p<∞$0<p<\infty$.     

Products of Toeplitz and Hankel Operators on Fock-Sobolev Spaces

In this paper, the authors investigate the boundedness of Toeplitz product T_f T_g and Hankel product H^*_fH_g on Fock-Sobolev space for f, g ∈ P. As a result, the boundedness of Toeplitz operator T_f and Hankel operator H_g with f ∈ P is characterized.     

Trace class Toeplitz operators with unbounded symbols on weighted Bergman spaces

In this note we construct a function φ in L2（Bn,dμ） which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on weighted Bergman space Lα2（Bn,dμ） for several complex variables.     

Schatten-Herz type positive Toeplitz operators on pluriharmonic Bergman spaces

Recently, Schatten-Herz type Toeplitz operators have been studied on the Bergman spaces and the harmonic Bergman spaces. Motivated these results, we study characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions on the ball of pluriharmonic Bergman spaces.     

Mixed Product of Hankel and Toeplitz Operators on Fock-Sobolev Spaces

Let f and g be functions in Fock-Sobolev space F^2,m. In this paper, we completely characterize the boundedness and compactness of H_f T_g.     

Commuting dual Toeplitz operators with pluriharmonic symbols

In this paper we completely characterize commuting dual Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball. We show that for φ and ψ pluriharmonic, SφSψ=Sψφ on only in the trivial case. Here the trivial case is φ or holomorphic.     

Toeplitz operators with BMO symbols of several complex variables

In this note we prove that the boundedness and compactness of the Toeplitz operator on the Bergman space L_a² (\mathbbB_n )L_a^2 (\mathbb{B}_n ) for several complex variables with a BMO¹ symbol is completely determined by the boundary behavior of its Berezin transform.     

Compact Toeplitz operators on the weighted Dirichlet space

In this paper, we completely characterize the compactness of Toeplitz operators with continuous symbol on the weighted Dirichlet space.     

Commuting Toeplitz operators with pluriharmonic symbols

By making use of -harmonic function theory, we characterize commuting Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball or on the Hardy space of the unit sphere in -dimensional complex space.

     

Hyponormality of Toeplitz operators with generalized circulant symbols

In this paper we obtain a necessary and sufficient condition for Toeplitz operators with generalized circulant symbols to be hyponormal.     

S_p-CLASS（0〈p〈∞）TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE

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相似文献   

Toeplitz operators with unbounded symbols of several complex variables

In this note we construct a function φ in L²(Bn,dA) which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on Bergman space for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L¹ symbols.     

Berezin transform and Toeplitz operators on harmonic Bergman spaces

For an operator which is a finite sum of products of finitely many Toeplitz operators on the harmonic Bergman space over the half-space, we study the problem: Does the boundary vanishing property of the Berezin transform imply compactness? This is motivated by the Axler-Zheng theorem for analytic Bergman spaces, but the answer would not be yes in general, because the Berezin transform annihilates the commutator of any pair of Toeplitz operators. Nevertheless we show that the answer is yes for certain subclasses of operators. In order to do so, we first find a sufficient condition on general operators and use it to reduce the problem to whether the Berezin transform is one-to-one on related subclasses.     

Segal-Bargmann空间上带无界符号的Toeplitz算子

In this paper,we construct a function φ in L2(Cn,d Vα) which is unbounded on any neighborhood of each point in Cnsuch that Tφ is a trace class operator on the SegalBargmann space H2(Cn,d Vα).In addition,we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H2(Cn,d Vα).     

Banach space structure of weighted Fock-Sobolev spaces

We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces F _α,s ^p , mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ‘nice’ functions in two different ways.     

Toeplitz operators on the polydisk

In this paper it is shown that two analytic Toeplitz operators essentially doubly commute if and only if they doubly commute on the Bergman space of the polydisk.

     

多圆盘上对偶Toeplitz算子的性质

本文研究了多圆盘上对偶Toeplitz算子的有界性、紧性和谱的特征。