The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu...The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f...For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.展开更多
In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
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 som...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.展开更多
In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-c...In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-commutators of two Toeplitz operators with quasi- homogeneous symbols.展开更多
Let p 〉 0 and μ be a normal function on [0, 1）, u（r） = （1 - r2）1＋n^pμ（r） for r ∈ [0, 1）. In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space AP（p） to t...Let p 〉 0 and μ be a normal function on [0, 1）, u（r） = （1 - r2）1＋n^pμ（r） for r ∈ [0, 1）. In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space AP（p） to the normal weight Bloch type space β （r）in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from A^p（μ） to βv, is given. At the same time, the authors give the briefly sufficient and necessary condition that Cv is compact on βμ, for a 〉 1.展开更多
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 consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in...In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2.展开更多
In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the sy...In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.展开更多
We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for t...We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for the proof of the boundedness of composition operators,and then obtain an upper bound for the special operator norm on Bergman space.展开更多
Let_(φ)and_(ψ)be linear fractional self-maps of the unit diskDandX_(a)separable Hilbert space.In this paper we completely characterize the weak compactness of the product operators of a composition operationC_(φ)wi...Let_(φ)and_(ψ)be linear fractional self-maps of the unit diskDandX_(a)separable Hilbert space.In this paper we completely characterize the weak compactness of the product operators of a composition operationC_(φ)with another one's adjointC_(ψ)^(*)on the vector-valued Bergman spaceB_(1)(X)for formsC_(φ)C_(ψ)^(*)andC_(ψ)C_(φ)^(*).展开更多
We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of powers of Toeplitz operators.We first charactreize analytic sy...We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of powers of Toeplitz operators.We first charactreize analytic symbolsφfor which the sequence Tφ*kf or Tφkf converges to 0 or∞as k→∞in norm for every nonzero Bergman function f.Also,we characterize analytic symbolsφfor which the norm of such a sequence is summable or not summable.We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.展开更多
This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition o...This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.展开更多
In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz oper...In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonie Bergman space.展开更多
In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa...In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa（Ω,dvβ）if and only if K（φ（z）,φ（z））/K（z,z）→0 as z→ Ω under a mild condition,where K（z,w）is the Bergman kernel.展开更多
In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball i...In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.展开更多
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
文摘For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
基金supported by the Natural Science Foundation of China(12271134)the Shanxi Scholarship Council of China(2020–089)the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(20200019).
文摘In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
基金the NNSF of China(10571164)the SRFDP of Higher Education(20050358052)
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127105911301047)the Scientific Research Found of Higher School of Inner Mongolia(Grant No.NJZY 13298)
文摘In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-commutators of two Toeplitz operators with quasi- homogeneous symbols.
基金supported by the National Natural Science Foundation of China(11571104)Hunan Provincial Natural Science Foundation of China(2015JJ2095)
文摘Let p 〉 0 and μ be a normal function on [0, 1）, u（r） = （1 - r2）1＋n^pμ（r） for r ∈ [0, 1）. In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space AP（p） to the normal weight Bloch type space β （r）in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from A^p（μ） to βv, is given. At the same time, the authors give the briefly sufficient and necessary condition that Cv is compact on βμ, for a 〉 1.
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 the Education Department Important Foundation of Hunan Province in China(10A074)supported by the Education Department Important Foundation of Hunan Provincein China(12A206)College of Mathematics and Computer Science,Key Laboratory of High Performance Computing and Stochastic Information Processing(Ministry of Education of China),Hunan Normal University,and the Construct Program of the Key Discipline in Hunan Province
文摘Let μ be a normal function on [0, 1）. The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p 〉 0.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2009-0093827)
文摘In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2.
基金This work was supported by the NSF (19971061) of China and the Science Foundation ofFushun Petroleum Institute.
文摘In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(13ZB0101)
文摘We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for the proof of the boundedness of composition operators,and then obtain an upper bound for the special operator norm on Bergman space.
基金Supported by the National Natural Science Foundation of China(19771063)
文摘Let_(φ)and_(ψ)be linear fractional self-maps of the unit diskDandX_(a)separable Hilbert space.In this paper we completely characterize the weak compactness of the product operators of a composition operationC_(φ)with another one's adjointC_(ψ)^(*)on the vector-valued Bergman spaceB_(1)(X)for formsC_(φ)C_(ψ)^(*)andC_(ψ)C_(φ)^(*).
基金supported by NSFC(11771401)the last author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1I1A3A01041943)。
文摘We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of powers of Toeplitz operators.We first charactreize analytic symbolsφfor which the sequence Tφ*kf or Tφkf converges to 0 or∞as k→∞in norm for every nonzero Bergman function f.Also,we characterize analytic symbolsφfor which the norm of such a sequence is summable or not summable.We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.
基金Supported by the NNSF of China(10471039)the Natural Science Foundation of Zhejiang Province(M103 104)the Natural Science Foundation of Huzhou City(2005YZ02).
文摘This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.
基金Supported by Innovation Program of Shanghai Municipal Education Commission(Grant No.13YZ090)
文摘In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonie Bergman space.
基金Supported by the National Natural Science Foundation of China (10771064)Natural Science Foundation of Zhejiang Province (Y7080197, Y6090036, Y6100219)+1 种基金Foundation of Creative Group in Colleges and Universities of Zhejiang Province (T200924)Foundation of Department of Education of Zhejiang province (20070482)
文摘In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa（Ω,dvβ）if and only if K（φ（z）,φ（z））/K（z,z）→0 as z→ Ω under a mild condition,where K（z,w）is the Bergman kernel.
基金supported by the National Natural Science Foundation of China (11171255,11101279)the Natural Science Foundation of Shanghai (13ZR1444100)
文摘In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.
