We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s 1). This result plays an important role in proving a necessary and sufficient condit...We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s 1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.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
In this paper, necessary and sufficient conditions for a closed range composition operator CФ on the general family of holomorphic function spaces F(p,q,s) and more generally on α-Besov type spaces F(p,αp-2,s) ...In this paper, necessary and sufficient conditions for a closed range composition operator CФ on the general family of holomorphic function spaces F(p,q,s) and more generally on α-Besov type spaces F(p,αp-2,s) are given. We give a Carleson measure characterization on F (p, αp - 2, s) spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of CФ on F(p,q,s) and F(p,αp- 2,s) spaces.展开更多
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit p...We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide "computable" estimates on the operator norm.展开更多
For all 0 〈 p, q 〈 ∞, let Cφ denote the composition operator from q-Bloch spaces βp to little p-Bloch spaces β0q on the unit ball of C^n. In this article, necessary and sufficient conditions for Cφ to be a boun...For all 0 〈 p, q 〈 ∞, let Cφ denote the composition operator from q-Bloch spaces βp to little p-Bloch spaces β0q on the unit ball of C^n. In this article, necessary and sufficient conditions for Cφ to be a bounded or compact operator are given.展开更多
In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.
This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to ...This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞( or little Bers-type spaces Hv,o∞ ), where v is normal.展开更多
In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the comple...In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the complex plane C.展开更多
In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces Λα (α 〉 1) of holomorphic functions in the unit disk are characterized.
In this paper, two problems about composition operator on Hardy space are considered. Firstly, a new estimation of the norm of a class of composition operators is given. Secondly, the cyclic behavior of the adjoint op...In this paper, two problems about composition operator on Hardy space are considered. Firstly, a new estimation of the norm of a class of composition operators is given. Secondly, the cyclic behavior of the adjoint operator of a composition operator is discussed.展开更多
We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2...In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2 and 2k < T 2k + 1 (or 2k - 1 < T 2k) for some positive integer k. Suppose = ( 1,… , n) be a univalent mapping from B into itself, denote dμj(l) (z) = R(l) j (z) 2(k-l+2) (1 - z 2)2k-t+1dv(z) for l= 1, 2,… , k + 1. If μj(l)-1 are (T - 2k + 2l-4)-Carleson measures for all l, then the composition operator C on DT is bounded; (ii) Let 1 < T n + 2, = ( 1,… , n) be univalent and the Frechet derivative of -1 be bounded on (B). If R j ∈ M(DT-2) for all j, then the composition operator C on DT is bounded; (iii) Let T > n + 2 and as in (ii). If j ∈ DT for all j, then the composition operator C on DT is bounded.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
Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T (Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math....Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T (Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math. Soc., 2014,46: 847-856), this paper shows that a bounded weighted composition operator onthe Fock space is a Fredholm operator if and only if it is an invertible operator, andif and only if it is a nonzero constant multiple of a unitary operator. The result isvery different from the corresponding results on the Hardy space and the Bergmanspace.展开更多
When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and...When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and compactness of composition operators from the space B0 to QK and QK,0.展开更多
Abstract: We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss ...Abstract: We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.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
For α ∈ (0, ∞), let Hα∞ (or Hα,0∞) denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|2)α = O(1) (or |f(z)|(1 - |z|2)α = o(1) as |z| → 1). Hα∞(or Hα,0∞...For α ∈ (0, ∞), let Hα∞ (or Hα,0∞) denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|2)α = O(1) (or |f(z)|(1 - |z|2)α = o(1) as |z| → 1). Hα∞(or Hα,0∞) is called a Bers-type space (or a little Bers-type space).In this paper, we give some basic properties of Hα∞. C, the composition operator associated with a symbol function which is an analytic self map of D, is difined by Cf = f o . We characterize the boundedness and compactness of C which sends one Bers-type space to another function space.展开更多
基金Supported by the National Natural Science Foundation of China (10971219)Shanghai Education Research and Innovation Project (10YZ185)Shanghai University Research Special Foundation for Outstanding Young Teachers (sjr09015)
文摘We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s 1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
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.
文摘In this paper, necessary and sufficient conditions for a closed range composition operator CФ on the general family of holomorphic function spaces F(p,q,s) and more generally on α-Besov type spaces F(p,αp-2,s) are given. We give a Carleson measure characterization on F (p, αp - 2, s) spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of CФ on F(p,q,s) and F(p,αp- 2,s) spaces.
文摘We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide "computable" estimates on the operator norm.
文摘For all 0 〈 p, q 〈 ∞, let Cφ denote the composition operator from q-Bloch spaces βp to little p-Bloch spaces β0q on the unit ball of C^n. In this article, necessary and sufficient conditions for Cφ to be a bounded or compact operator are given.
基金Supported in part by the National Natural Science Foundation of China(1130140411271359)the Educational Commission of Hubei Province of China(Q20121503)
文摘In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.
基金Supported by the National Natural Science Foundation of China (10771064)the Natural Science Foundation of Zhejiang province (Y6090036+1 种基金Y7080197,Y606197)the Foundation of Department of Education of Zhejiang Province (20070482)
文摘This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞( or little Bers-type spaces Hv,o∞ ), where v is normal.
文摘In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the complex plane C.
基金Supported in part by the National Natural Science Foundation of China (10971219)
文摘In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces Λα (α 〉 1) of holomorphic functions in the unit disk are characterized.
基金This research is supported by the NNSF of China (10401027)
文摘In this paper, two problems about composition operator on Hardy space are considered. Firstly, a new estimation of the norm of a class of composition operators is given. Secondly, the cyclic behavior of the adjoint operator of a composition operator is discussed.
基金This work was supported by NSF of China(11171203,11201280)New Teacher’s Fund for Doctor Stations,Ministry of Education(20114402120003)NSF of Guangdong Province(10151503101000025,S2011010004511,S2011040004131)
文摘We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
基金the Natural Science Foundation of Guangdong Province.
文摘In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2 and 2k < T 2k + 1 (or 2k - 1 < T 2k) for some positive integer k. Suppose = ( 1,… , n) be a univalent mapping from B into itself, denote dμj(l) (z) = R(l) j (z) 2(k-l+2) (1 - z 2)2k-t+1dv(z) for l= 1, 2,… , k + 1. If μj(l)-1 are (T - 2k + 2l-4)-Carleson measures for all l, then the composition operator C on DT is bounded; (ii) Let 1 < T n + 2, = ( 1,… , n) be univalent and the Frechet derivative of -1 be bounded on (B). If R j ∈ M(DT-2) for all j, then the composition operator C on DT is bounded; (iii) Let T > n + 2 and as in (ii). If j ∈ DT for all j, then the composition operator C on DT is bounded.
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.
文摘Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T (Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math. Soc., 2014,46: 847-856), this paper shows that a bounded weighted composition operator onthe Fock space is a Fredholm operator if and only if it is an invertible operator, andif and only if it is a nonzero constant multiple of a unitary operator. The result isvery different from the corresponding results on the Hardy space and the Bergmanspace.
基金Foundation item: Supported by the Natural Science Foundation of China(10471039) Supported by the Natural Science Foundation of the Education Committee of Jiangsu Province of China(06KJD110175+1 种基金 07KJB110115) Supported by the Scientific Research Foundation of Xuzhou professional of Architectural Technologies(07JYA3-13) Acknowledgment The authors thank the referees and the editors for good advice on this paper. The second author also thanks professors Shaozong Yan and Xiaoman Chen for their encouragement and help while visiting in Fudan university.
文摘When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and compactness of composition operators from the space B0 to QK and QK,0.
基金The NSF(11501136,11271092)of Chinathe Key Discipline Construction Project of Subject Groups Focus on Mathematics+1 种基金Information Science in the Construction Project(4601-2015)of the High-level University of Guangdong Provincethe Project(HL02-1517)for the New Talent of Guangzhou University
文摘Abstract: We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.
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.
文摘For α ∈ (0, ∞), let Hα∞ (or Hα,0∞) denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|2)α = O(1) (or |f(z)|(1 - |z|2)α = o(1) as |z| → 1). Hα∞(or Hα,0∞) is called a Bers-type space (or a little Bers-type space).In this paper, we give some basic properties of Hα∞. C, the composition operator associated with a symbol function which is an analytic self map of D, is difined by Cf = f o . We characterize the boundedness and compactness of C which sends one Bers-type space to another function space.