In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In additio...In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.展开更多
Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and o...Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.展开更多
In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz op...In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz operators. Then we obtain spectral properties of dual Toeplitz operators. Finally, we show that there are no quasinormal dual Toeplitz operators with bounded holomorphic or anti-holomorphic symbols.展开更多
Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reprodu...Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reproducing kernels. These results have been shown for Toeplitz operators on the Paley-Wiener space, a reproducing kernel Hilbert space over C. Furthermore, we show how the norm of such an operator has no relation to the supremum of the norms of the pictures of the normalization reproducing kernels of the space. As a result, if this supremum is finite, the operator is implicitly bounded. To further demonstrate that the operator norm is not the same as the supremum of the norms of the pictures of the real normalized reproducing kernels, another example is also provided. We also set out a necessary and sufficient condition for the operators’ compactness in terms of their limiting function on the reproducing kernels.展开更多
In this paper,we introduce and investigate certain subclass of analytic and univalent functions involving q-differintegral operator.For this function class,we give the bound estimates of the coefficients a2 and a3 and...In this paper,we introduce and investigate certain subclass of analytic and univalent functions involving q-differintegral operator.For this function class,we give the bound estimates of the coefficients a2 and a3 and some Fekete-Szegöfunctional inequalities.Besides,we also estimate the corresponding symmetric Toeplitz determinants.Furthermore,we point out some consequences and connections to these results above.展开更多
In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz oper...In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.展开更多
A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space.In this paper we prove a neces...A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space.In this paper we prove a necessary and sufficient condition for the commutator of two truncated Toeplitz operators on a model space to be compact.展开更多
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 ...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.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
In this paper, we investigate the semi-commutators of Toeplitz operators on the weighted Bergman spaces Ap(?), and characterize the bounded harmonic functions u and v on the unit disk for which the semi-commutator of ...In this paper, we investigate the semi-commutators of Toeplitz operators on the weighted Bergman spaces Ap(?), and characterize the bounded harmonic functions u and v on the unit disk for which the semi-commutator of Toeplitz operators Tu and Tv is 0 or compact operator.展开更多
In this paper, a general function space X（B n ） over the unit ball in C n with norm · X（Bn） is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a comp...In this paper, a general function space X（B n ） over the unit ball in C n with norm · X（Bn） is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X（B n ）, related to works of [8] and [10].展开更多
We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equival...We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.展开更多
In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Diric...In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces展开更多
In this paper, we study some algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space of the unit disk.
Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the B...Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the Berezin transform S(z) of S tends to zero as z→Ω.展开更多
In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not h...In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .展开更多
In the setting of Fock-Sobolev spaces of positive orders over the complex plane,Choe and Yang showed that if the one of the symbols of two commuting Toeplitz operators with bounded symbols is non-trivially radial,then...In the setting of Fock-Sobolev spaces of positive orders over the complex plane,Choe and Yang showed that if the one of the symbols of two commuting Toeplitz operators with bounded symbols is non-trivially radial,then the other must also be radial.In this paper,we extend this result to the Fock-Sobolev space of negative order using the Fock-type space with a confluent hyper geometric function.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11271092)the Natural Science Foundation of Guangdong Province(Grant No.S2011010005367)
文摘In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.
基金Supported by Doctoral Program Foundation of Higher Education.
文摘Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501075,11271059)the Natural Science Foundation of Liaoning Education Department(Grant No.L2015084)the Natural Science Foundation of Guangxi Education Department(Grant No.KY2015LX518)
文摘In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz operators. Then we obtain spectral properties of dual Toeplitz operators. Finally, we show that there are no quasinormal dual Toeplitz operators with bounded holomorphic or anti-holomorphic symbols.
文摘Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reproducing kernels. These results have been shown for Toeplitz operators on the Paley-Wiener space, a reproducing kernel Hilbert space over C. Furthermore, we show how the norm of such an operator has no relation to the supremum of the norms of the pictures of the normalization reproducing kernels of the space. As a result, if this supremum is finite, the operator is implicitly bounded. To further demonstrate that the operator norm is not the same as the supremum of the norms of the pictures of the real normalized reproducing kernels, another example is also provided. We also set out a necessary and sufficient condition for the operators’ compactness in terms of their limiting function on the reproducing kernels.
基金Supported by Natural Science Foundation of Ningxia(Grant No.2023AAC03001)Natural Science Foundation of China(Grant No.12261068).
文摘In this paper,we introduce and investigate certain subclass of analytic and univalent functions involving q-differintegral operator.For this function class,we give the bound estimates of the coefficients a2 and a3 and some Fekete-Szegöfunctional inequalities.Besides,we also estimate the corresponding symmetric Toeplitz determinants.Furthermore,we point out some consequences and connections to these results above.
文摘In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.
文摘A model space is a subspace of the Hardy space which is invariant under the backward shift,and a truncated Toeplitz operator is the compression of a Toeplitz operator on some model space.In this paper we prove a necessary and sufficient condition for the commutator of two truncated Toeplitz operators on a model space to be compact.
基金Supported by National Natural Science Foundation of China (Grant No. 10671042)Research Fund for Doctoral Program of Higher Education
文摘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.
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.
文摘In this paper, we investigate the semi-commutators of Toeplitz operators on the weighted Bergman spaces Ap(?), and characterize the bounded harmonic functions u and v on the unit disk for which the semi-commutator of Toeplitz operators Tu and Tv is 0 or compact operator.
文摘In this paper, a general function space X（B n ） over the unit ball in C n with norm · X（Bn） is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X（B n ）, related to works of [8] and [10].
基金supported by National Natural Science Foundation of China (Grant Nos.11271092 and 11301101)Guangzhou Higher Education Science and Technology Project (Grant No.2012A018)
文摘We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.
基金Project was partly supported by NKBRSF(C1998030600)NSF of China(60073038)the Doctoral Program Foundation of Educational Department of China (1999014115)the outstanding Young Teacher Foundation of Educational Department of China.
文摘In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces
基金Supported by NSFC(Grant Nos.11471113,11271332 and 11431011)Zhejiang Provincial SFC(Grant Nos.LY14A010013 and LY13A010021)the Fundamental Research Funds for the Central Universities
文摘In this paper, we study some algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space of the unit disk.
文摘Let Ω be the unit ball or the polydisk of Cnand L2a(Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on L2a( Ω), then S is compact if and only if the Berezin transform S(z) of S tends to zero as z→Ω.
基金supported by National Natural Science Foundation of China(Grant No.11271387)Chongqing Natural Sience Foundation(Grant No.2013jjB 0050)Simons Foundation(Grant No.196300)
文摘In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .
基金supported by NRF of Korea(Grant No.NRF-2020R1F1A1A01048601)supported by NRF of Korea(Grant No.NRF-2020R1I1A1A01074837)。
文摘In the setting of Fock-Sobolev spaces of positive orders over the complex plane,Choe and Yang showed that if the one of the symbols of two commuting Toeplitz operators with bounded symbols is non-trivially radial,then the other must also be radial.In this paper,we extend this result to the Fock-Sobolev space of negative order using the Fock-type space with a confluent hyper geometric function.
