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.
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
We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the u...We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.展开更多
We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type inte...We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^(p) to weighted Bergman spaces A_(α)^(q) for the different values of p and q in the unit ball.展开更多
A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.
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
Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ...Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ with another one's adjoint C * ψ on the vector\|valued Bergman space B 1(X) for forms C φC * ψ and C * ψC φ.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
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
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 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
Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological conn...Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological connectedness of the set of composition operators on A_(ω)^(p).As an application,we construct an interesting example which reveals that two composition operators on A_(α)^(p) in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman space.In addition,we completely describe the central compactness of any finite linear combinations of composition operators on A_(ω)^(p) in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.展开更多
In this paper,we give a universal description of the boundedness and compactness of Toeplitz operator T_(μ)^(ω)between Bergman spaces A_(η)^(p)and A_(υ)^(q)whenμis a positive Borel measure,1<p,q<∞andω,η,...In this paper,we give a universal description of the boundedness and compactness of Toeplitz operator T_(μ)^(ω)between Bergman spaces A_(η)^(p)and A_(υ)^(q)whenμis a positive Borel measure,1<p,q<∞andω,η,υare regular weights.By using Khinchin’s inequality and Kahane’s inequality,we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.展开更多
We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0<p,q<∞.For the case n=1,some partial results were previously obtain...We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0<p,q<∞.For the case n=1,some partial results were previously obtained by Wu in[Wu,Z.:Volterra operator,area integral and Carleson measures,Sci.China Math.,54,2487–2500(2011)].Especially,in the case q<p and q<s,we obtain some characterizations for the area operators to be bounded.We solve the cases left open there and extend the results to n-complex dimension.展开更多
In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a...In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.展开更多
In this paper, we express the essential norms of composition operators between weighted Bergman spaces of the unit disc in terms of the generalized Nevanlinna counting function.
The authors obtain function theoretic characterizations of the compactness on the standardweighted Bergman spaces of the two operators formed by multiplying a composition operatorwith the adjoint of another compositio...The authors obtain function theoretic characterizations of the compactness on the standardweighted Bergman spaces of the two operators formed by multiplying a composition operatorwith the adjoint of another composition operator.展开更多
In this paper,we study some properties of weighted composition operators on a class of weighted Bergman spaces Ap with O<p≤∝ and φ∈Wo.Also,we completely characterize the q-Carleson measure for Ap in terms of th...In this paper,we study some properties of weighted composition operators on a class of weighted Bergman spaces Ap with O<p≤∝ and φ∈Wo.Also,we completely characterize the q-Carleson measure for Ap in terms of the averaging function and the generalized Berezin transform with 0<q<∝.As applications,the boundedness and compactness of weighted composition operators acting from one Bergman space A^(p)_(φ) to another Ag are equivalently described and the Schatten class property of the weighted composition operator acting on A^(2)_(φ) are given.Our main results are expressed in terms of certain Berezin type integral transforms.展开更多
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.
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.
文摘We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.
基金supported by the National Natural Science Foundation of China(11771441 and 11601400)。
文摘We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^(p) to weighted Bergman spaces A_(α)^(q) for the different values of p and q in the unit ball.
基金This paper is a part of the author's series of letures at the Mathematical Institute of the Hungarian Academy of Sciences while visiting Hungary sent by the state Education Committee,the People's Republic of China.
文摘A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.
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.
文摘Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ with another one's adjoint C * ψ on the vector\|valued Bergman space B 1(X) for forms C φC * ψ and C * ψC φ.
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 (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.
基金supported by National Natural Science Foundation of China (Grant Nos. 12101467 and 12171373)。
文摘Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological connectedness of the set of composition operators on A_(ω)^(p).As an application,we construct an interesting example which reveals that two composition operators on A_(α)^(p) in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman space.In addition,we completely describe the central compactness of any finite linear combinations of composition operators on A_(ω)^(p) in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.
基金supported by NNSF of China(Grant No.12271328)Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012117)+1 种基金Projects of Talents Recruitment of GDUPT(Grant No.2022rcyj2008)supported by STU Scientific Research Initiation Grant(Grant No.NTF23004)。
文摘In this paper,we give a universal description of the boundedness and compactness of Toeplitz operator T_(μ)^(ω)between Bergman spaces A_(η)^(p)and A_(υ)^(q)whenμis a positive Borel measure,1<p,q<∞andω,η,υare regular weights.By using Khinchin’s inequality and Kahane’s inequality,we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.
基金partially supported by NSFC(Grant Nos.12171150,11771139)partially supported by NSFC(Grant Nos.12171373,12371136)+2 种基金ZJNSF(Grant No.LY20A010008)supported by the grants MTM2017-83499-P(Ministerio de Educación y Ciencia)2017SGR358(Generalitat de Catalunya)。
文摘We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0<p,q<∞.For the case n=1,some partial results were previously obtained by Wu in[Wu,Z.:Volterra operator,area integral and Carleson measures,Sci.China Math.,54,2487–2500(2011)].Especially,in the case q<p and q<s,we obtain some characterizations for the area operators to be bounded.We solve the cases left open there and extend the results to n-complex dimension.
基金supported by the National Natural Science Foundation of China(12271101)。
文摘In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.
基金Supported by National Natural Science Foundation of China(Grant Nos.11071230 and 11171318)Natural Science Foundation of Anhui Province(Grant No.090416233)
文摘In this paper, we express the essential norms of composition operators between weighted Bergman spaces of the unit disc in terms of the generalized Nevanlinna counting function.
文摘The authors obtain function theoretic characterizations of the compactness on the standardweighted Bergman spaces of the two operators formed by multiplying a composition operatorwith the adjoint of another composition operator.
基金Supported by the National Natural Science Foundation of China (Grant Nos.12071155,11871170)the open project of Key Laboratory,School of Mathematical Sciences,Chongqing Normal University (Grant No.CSSXKFKTM202002)the Innovation Research for the Postgraduates of Guangzhou University (Grant No.2020GDJC-D08).
文摘In this paper,we study some properties of weighted composition operators on a class of weighted Bergman spaces Ap with O<p≤∝ and φ∈Wo.Also,we completely characterize the q-Carleson measure for Ap in terms of the averaging function and the generalized Berezin transform with 0<q<∝.As applications,the boundedness and compactness of weighted composition operators acting from one Bergman space A^(p)_(φ) to another Ag are equivalently described and the Schatten class property of the weighted composition operator acting on A^(2)_(φ) are given.Our main results are expressed in terms of certain Berezin type integral transforms.
