Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference...Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.展开更多
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).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
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
In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions...In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved.展开更多
In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on comp...In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.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
This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces.Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions for...This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces.Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions for composition operator sequences to be collectively compact between weighted Bergman spaces are given.展开更多
In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （...In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.展开更多
Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz opera...Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO(R^n) function and T~α.展开更多
In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operat...In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.展开更多
It is proven that there exists a Dedekind complete Banach lattice E such that the linear spans/f （E） and IV （E） of positive compact and positive weakly compact operators on E fails to possess the Riesz separation ...It is proven that there exists a Dedekind complete Banach lattice E such that the linear spans/f （E） and IV （E） of positive compact and positive weakly compact operators on E fails to possess the Riesz separation property.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
In this paper, we study the compact operators on weighted Bergman spaces of the unit ball. Extending Miao and Zheng＇result in 2004, we obtain the necessary and sufficient conditions for the operator to be compact on ...In this paper, we study the compact operators on weighted Bergman spaces of the unit ball. Extending Miao and Zheng＇result in 2004, we obtain the necessary and sufficient conditions for the operator to be compact on weighted Bergman spaces of the unit ball under some integrable conditions.展开更多
There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent result...There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent results in this area.展开更多
In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth...In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.展开更多
： We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in B∞（Ω） and certain operator have a small compact perturbation wh...： We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in B∞（Ω） and certain operator have a small compact perturbation which is a strongly irreducible operator in B∞（Ω）？ In this paper, we prove that the direct sum of any strongly irreducible operator in B∞（Ω） and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators in B∞（Ω）.展开更多
Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of t...Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).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
基金supported by National Science Foundations of China(Grant No.11771340,12171373).
文摘Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
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.
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.
基金Supported by the Natural Science Foundation of Shandong Province(Nos.ZR2018PA004 and ZR2016AB07)the National Natural Science Foundation of China(Nos.11571306 and 11671363)
文摘In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved.
文摘In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.
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This research is supported by the National Natural Science Foundation of China
文摘This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces.Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions for composition operator sequences to be collectively compact between weighted Bergman spaces are given.
基金supported by the research project#144003 of the Serbian Ministry of Science, Technology and Development
文摘In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.
基金supported by the NNSF of China(11571306)supported by the NNSF of China(11271330 and 11671363)supported by the NNSF of China(11371370)
文摘Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO(R^n) function and T~α.
文摘In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.
文摘It is proven that there exists a Dedekind complete Banach lattice E such that the linear spans/f （E） and IV （E） of positive compact and positive weakly compact operators on E fails to possess the Riesz separation property.
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 the National Natural Science Foundation of China (Grant Nos. 1067102810971020)
文摘In this paper, we study the compact operators on weighted Bergman spaces of the unit ball. Extending Miao and Zheng＇result in 2004, we obtain the necessary and sufficient conditions for the operator to be compact on weighted Bergman spaces of the unit ball under some integrable conditions.
文摘There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent results in this area.
文摘In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.
基金The Specialized Research Fund (20050183002) for the Doctoral Program of Higher Educationthe NNSF (10371049 and J0630104) of China.
文摘： We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in B∞（Ω） and certain operator have a small compact perturbation which is a strongly irreducible operator in B∞（Ω）？ In this paper, we prove that the direct sum of any strongly irreducible operator in B∞（Ω） and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators in B∞（Ω）.
文摘Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).
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.
