In this paper,we study the boundedness and compactness of composition operator C<sub> </sub>on the Bloch space β（Ω）,Ω being a bounded homogeneous domain.For Ω=B<sub>n</sub>,we give the ne...In this paper,we study the boundedness and compactness of composition operator C<sub> </sub>on the Bloch space β（Ω）,Ω being a bounded homogeneous domain.For Ω=B<sub>n</sub>,we give the necessary and sufficient conditions for a composition operator C<sub> </sub>to be compact on β（B<sub>n</sub>）or β<sub>0</sub>（B<sub>n</sub>）.展开更多
We characterize those holomorphic mappings (?) from the polydisc Dn in Cn to itself for which the induced composition operators C(?) are bounded (or compact) from the Bloch-type space Bω to Bμ (respectively, from th...We characterize those holomorphic mappings (?) from the polydisc Dn in Cn to itself for which the induced composition operators C(?) are bounded (or compact) from the Bloch-type space Bω to Bμ (respectively, from the little Bloch-type space Bω,0 to Bμ,0), where ω is a normal function on [0,1) and μ is a nonnegative function on [0,1) with μ(tn) > 0 for some sequence {tn}n=1∞(?)[0,1) satisfying limn→∞ tn = 1.展开更多
Let Un be the unit polydisc of ?n and φ=(φ1, ?, φ n ) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for ...Let Un be the unit polydisc of ?n and φ=(φ1, ?, φ n ) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for every ε > 0, there exists a δ > 0, such that $$\sum\limits_{k,1 = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial z_k }}(z)} \right|} \frac{{1 - |z_k |^2 }}{{1 - |\phi _l (z)|^2 }}< \varepsilon ,$$ whenever dist(φ(z), ?U n )<δ.展开更多
Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） f...Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） for 0 ≤ r 〈 Cφ. Our compactness condition depends only on Φ which can be considered as a slight improvement of the known results. The compactness of Cφ from the Dirichlet space D into the spaces QK is also investigated,展开更多
In this paper,we prove that a composition operator on H^P(B)is Fredholm if and only if it is invertible if and only if its symbol is an automorphism on B,and give the representation of the spectra of a class of compos...In this paper,we prove that a composition operator on H^P(B)is Fredholm if and only if it is invertible if and only if its symbol is an automorphism on B,and give the representation of the spectra of a class of composition operators.In addition,using composition operator,we discuss intertwining Toeplitz operators.展开更多
Let Un be the unit polydisc of Cn and φ = (φ 1,...,φ n ) a holomorphic self-map of Un. Let 0 ≤α 1. This paper shows that the composition operator C is bounded on the Lipschitz space Lip(Un) if and only if there e...Let Un be the unit polydisc of Cn and φ = (φ 1,...,φ n ) a holomorphic self-map of Un. Let 0 ≤α 1. This paper shows that the composition operator C is bounded on the Lipschitz space Lip(Un) if and only if there exists M > 0 such that $$\sum\limits_{k,l = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial zk}}(z)} \right|\left( {\frac{{1 - \left| {z_k } \right|^2 }}{{1 - \left| {\phi _l (z)} \right|^2 }}} \right)^{1 - \alpha } } \leqslant M$$ for z ∈ Un. Moreover Cφ is compact on Lipα(Un) if and only if Cφ is bounded on Lipα(Un) and for every ε>0, there exists a δ > 0 such that $$\sum\limits_{k,l = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial zk}}(z)} \right|\left( {\frac{{1 - \left| {z_k } \right|^2 }}{{1 - \left| {\phi _l (z)} \right|^2 }}} \right)^{1 - \alpha } } \leqslant \varepsilon $$ whenever dist((z),?Un).展开更多
In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the compositio...In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the composition operator to be compact on the Bloch space in a bounded symmetric domain.展开更多
This paper proves that a necessary condition for a composition operator on the Bloch space of the unit disk to be bounded below given by Ghatage, Yan and Zheng is also sufficient. Given furthermore are a sufficient co...This paper proves that a necessary condition for a composition operator on the Bloch space of the unit disk to be bounded below given by Ghatage, Yan and Zheng is also sufficient. Given furthermore are a sufficient condition and a necessary condition of the boundedness from below for a composition operator on the Bloch space of a unit ball with dimensions bigger than one.展开更多
In this paper,we study composition operators on a Banach space of analytic functions, denoted by X,which includes the Bloch space.This space arises naturally as the dual space of analytic functions in the Bergman spac...In this paper,we study composition operators on a Banach space of analytic functions, denoted by X,which includes the Bloch space.This space arises naturally as the dual space of analytic functions in the Bergman space L_a^1(D)which admit an atomic decomposition.We charac- terize the functions which induce compact composition operators and those which induce Fredholm operatorson this space.We also investigate when a composition operator has a closed range.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
基金Supported by the National Natural Science Foundation the National Education Committee Doctoral Foundation
文摘In this paper,we study the boundedness and compactness of composition operator C<sub> </sub>on the Bloch space β（Ω）,Ω being a bounded homogeneous domain.For Ω=B<sub>n</sub>,we give the necessary and sufficient conditions for a composition operator C<sub> </sub>to be compact on β（B<sub>n</sub>）or β<sub>0</sub>（B<sub>n</sub>）.
基金supported by the National Natural Science Foundation of China(Grant No.10471039)the Natural Science Foundation of Zhejiang Ptovince(Grant No.M103104).
文摘We characterize those holomorphic mappings (?) from the polydisc Dn in Cn to itself for which the induced composition operators C(?) are bounded (or compact) from the Bloch-type space Bω to Bμ (respectively, from the little Bloch-type space Bω,0 to Bμ,0), where ω is a normal function on [0,1) and μ is a nonnegative function on [0,1) with μ(tn) > 0 for some sequence {tn}n=1∞(?)[0,1) satisfying limn→∞ tn = 1.
基金This work was supported in part by the National Natural Science Foundation of China ( Grant No. 19871081).
文摘Let Un be the unit polydisc of ?n and φ=(φ1, ?, φ n ) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for every ε > 0, there exists a δ > 0, such that $$\sum\limits_{k,1 = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial z_k }}(z)} \right|} \frac{{1 - |z_k |^2 }}{{1 - |\phi _l (z)|^2 }}< \varepsilon ,$$ whenever dist(φ(z), ?U n )<δ.
基金the National Natural Science Foundation of China (No.10371069) and the NSF of Guangdong Province of China (No.04011000)
文摘Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） for 0 ≤ r 〈 Cφ. Our compactness condition depends only on Φ which can be considered as a slight improvement of the known results. The compactness of Cφ from the Dirichlet space D into the spaces QK is also investigated,
基金This research is supported in part from the National Natural Science Foundation of China (No.10371069)the NSF of Guangdong Province of China (No. 010446)
文摘In this paper,we prove that a composition operator on H^P(B)is Fredholm if and only if it is invertible if and only if its symbol is an automorphism on B,and give the representation of the spectra of a class of composition operators.In addition,using composition operator,we discuss intertwining Toeplitz operators.
基金This work was supported in part by the National Natural Science Foundation ofChina (Grant Nos. 19871081 & 10001030) LiuHui Center for Applied Mathematics, Nankai University and Tianjin University.
文摘Let Un be the unit polydisc of Cn and φ = (φ 1,...,φ n ) a holomorphic self-map of Un. Let 0 ≤α 1. This paper shows that the composition operator C is bounded on the Lipschitz space Lip(Un) if and only if there exists M > 0 such that $$\sum\limits_{k,l = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial zk}}(z)} \right|\left( {\frac{{1 - \left| {z_k } \right|^2 }}{{1 - \left| {\phi _l (z)} \right|^2 }}} \right)^{1 - \alpha } } \leqslant M$$ for z ∈ Un. Moreover Cφ is compact on Lipα(Un) if and only if Cφ is bounded on Lipα(Un) and for every ε>0, there exists a δ > 0 such that $$\sum\limits_{k,l = 1}^n {\left| {\frac{{\partial \phi _l }}{{\partial zk}}(z)} \right|\left( {\frac{{1 - \left| {z_k } \right|^2 }}{{1 - \left| {\phi _l (z)} \right|^2 }}} \right)^{1 - \alpha } } \leqslant \varepsilon $$ whenever dist((z),?Un).
基金supported in part by the National Natural Science Foundation of China(Grand No.10371091)LiuHui Center for Applied Mathematics,Nankai University&Tianjin University.
文摘In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the composition operator to be compact on the Bloch space in a bounded symmetric domain.
基金spporte in part by the National Natural Sience Poundaio of China(Grant No.19631140)
文摘This paper proves that a necessary condition for a composition operator on the Bloch space of the unit disk to be bounded below given by Ghatage, Yan and Zheng is also sufficient. Given furthermore are a sufficient condition and a necessary condition of the boundedness from below for a composition operator on the Bloch space of a unit ball with dimensions bigger than one.
文摘In this paper,we study composition operators on a Banach space of analytic functions, denoted by X,which includes the Bloch space.This space arises naturally as the dual space of analytic functions in the Bergman space L_a^1(D)which admit an atomic decomposition.We charac- terize the functions which induce compact composition operators and those which induce Fredholm operatorson this space.We also investigate when a composition operator has a closed range.
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.
