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
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
The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel ...The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.展开更多
In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten...In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.展开更多
In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class prop...In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class property criteria.On the eut-off c(N) we know that the phenomenon founded by Peloso is an exceptional case.展开更多
An extension of slant Hankel operator,namely,the kth-orderλ-slant Hankel operator on the Lebesgue space L^(2)(T^(n)),where T is the unit circle and n≥1,a natural number,is described in terms of the solution of a sys...An extension of slant Hankel operator,namely,the kth-orderλ-slant Hankel operator on the Lebesgue space L^(2)(T^(n)),where T is the unit circle and n≥1,a natural number,is described in terms of the solution of a system of operator equations,which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator.The study is further lifted in Calkin algebra in terms of essentially kth-orderλ-slant Hankel operators on L^(2)(T^(n)).展开更多
For two kind of MSebius invariant subspace A^α,d（D） and A^β,2 （D）, define the Toeplitz operators Tf^s and Hankel operators Hf^r on A^α,d（D）×A^β,2 （D） with an arbi-trary analytic ＂symbol function＂ f ...For two kind of MSebius invariant subspace A^α,d（D） and A^β,2 （D）, define the Toeplitz operators Tf^s and Hankel operators Hf^r on A^α,d（D）×A^β,2 （D） with an arbi-trary analytic ＂symbol function＂ f on a unit disk, and study their boundedness, compactness and Schatten-von Neumann properties.展开更多
For two kinds of the Moebius invariant subspace A_l^(a,2)(D) and A_l^(-a,2)(D) of L^(a,2)(D), we define big and small Hankel operators H_b^(ll') and h_b^(ll') for the analytic symbol function b(z), and st...For two kinds of the Moebius invariant subspace A_l^(a,2)(D) and A_l^(-a,2)(D) of L^(a,2)(D), we define big and small Hankel operators H_b^(ll') and h_b^(ll') for the analytic symbol function b(z), and study their boundedness, compactness and Schatten-von Neumanu classes S_p-estimates, and hence develope Schatten -von Neumann properties of these op- erators.展开更多
In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We sol...In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.展开更多
We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.
This paper is devoted to studying Bergman spaces A_(ω_(1,2))^(p)(M)(1<p<∞)induced by regular-weightω_(1,2) on annulus M.We characterize the function f in L_(ω1,2)^(1)(M)for which the induced Hankel operator ...This paper is devoted to studying Bergman spaces A_(ω_(1,2))^(p)(M)(1<p<∞)induced by regular-weightω_(1,2) on annulus M.We characterize the function f in L_(ω1,2)^(1)(M)for which the induced Hankel operator H_(f) is bounded(or compact)from A_(ω1,2)^(p)(M)to Lqω1,2(M)with 1<p,q<∞.展开更多
Extensions of the Hardy and the Bergman modules over the disc algebra are studied.The author relates extensions of these canonical modules to the symbol spaces of corresponding Hankel operators.In the context of funct...Extensions of the Hardy and the Bergman modules over the disc algebra are studied.The author relates extensions of these canonical modules to the symbol spaces of corresponding Hankel operators.In the context of function theory,an explicit formula of Ext(L^(2)_(a)(D),H^(2)(D))is obtained.Finally,it is also proved that Ext(L^(2)_(a)(D),L:(D))≠0.This may be the essential difference between the Hardy and the Bergman modules over the disk algebra.展开更多
In this paper the small Hankel operators on the Dirichlet-type spaces D p on the unit ball of C n are considered. A similar result to that of the one-dimensional setting is given, which characterizes the boundedness o...In this paper the small Hankel operators on the Dirichlet-type spaces D p on the unit ball of C n are considered. A similar result to that of the one-dimensional setting is given, which characterizes the boundedness of the small Hankel operators on D p .展开更多
The authors study the basic properties of Hankel operators and the structures of Hankel algebras relative to ordered groups,providing a new class of C*-algebras which are very useful in general C*-algebra theory.
We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We fu...We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We furthermore obtain necessary and sufficient conditions for bounded Haplitz products HfTg-,where f∈L2（Bn,dvα） and g is a square integrable holomorphic function.展开更多
Let S denote the class of functions that are analytic, normalized and univalent in the open unit disk E = {z: |z| S* and C respectively. A new subclass of analytic functions that generalize some known subclasses of an...Let S denote the class of functions that are analytic, normalized and univalent in the open unit disk E = {z: |z| S* and C respectively. A new subclass of analytic functions that generalize some known subclasses of analytic functions was defined and investigated. We obtained coefficient bounds, upper estimates for the Fekete-Szegö functional and the Hankel determinant.展开更多
We give a survey on the Berezin transform and its applications in operator theory. The focus is on the Bergman space of the unit disk and the Fock space of the complex plane. The Berezin transform is most effective an...We give a survey on the Berezin transform and its applications in operator theory. The focus is on the Bergman space of the unit disk and the Fock space of the complex plane. The Berezin transform is most effective and most successful in the study of Hankel and Toepltiz operators.展开更多
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(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.
文摘The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
文摘The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.
文摘In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.
文摘In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class property criteria.On the eut-off c(N) we know that the phenomenon founded by Peloso is an exceptional case.
文摘An extension of slant Hankel operator,namely,the kth-orderλ-slant Hankel operator on the Lebesgue space L^(2)(T^(n)),where T is the unit circle and n≥1,a natural number,is described in terms of the solution of a system of operator equations,which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator.The study is further lifted in Calkin algebra in terms of essentially kth-orderλ-slant Hankel operators on L^(2)(T^(n)).
文摘For two kind of MSebius invariant subspace A^α,d（D） and A^β,2 （D）, define the Toeplitz operators Tf^s and Hankel operators Hf^r on A^α,d（D）×A^β,2 （D） with an arbi-trary analytic ＂symbol function＂ f on a unit disk, and study their boundedness, compactness and Schatten-von Neumann properties.
文摘For two kinds of the Moebius invariant subspace A_l^(a,2)(D) and A_l^(-a,2)(D) of L^(a,2)(D), we define big and small Hankel operators H_b^(ll') and h_b^(ll') for the analytic symbol function b(z), and study their boundedness, compactness and Schatten-von Neumanu classes S_p-estimates, and hence develope Schatten -von Neumann properties of these op- erators.
基金Supported by National Natural Science Foundation of China(Grant No.11271059)
文摘In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.
基金supported by National Natural Science Foundation of China(Grant No.11771139)supported by Ministerio de Educación y Ciencia(Grant No.MTM2017-83499-P)Generalitat de Catalunya(Grant No.2017SGR358)。
文摘We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.
基金Supported by NNSF of China(Grant Nos.11971125,11471084)。
文摘This paper is devoted to studying Bergman spaces A_(ω_(1,2))^(p)(M)(1<p<∞)induced by regular-weightω_(1,2) on annulus M.We characterize the function f in L_(ω1,2)^(1)(M)for which the induced Hankel operator H_(f) is bounded(or compact)from A_(ω1,2)^(p)(M)to Lqω1,2(M)with 1<p,q<∞.
基金National Natural Science Foundation of ChinaMathematics Center of the Ministry of Education of ChinaLaboratory of Mathematics for Nonlinear Model and Methods at Fudan University.
文摘Extensions of the Hardy and the Bergman modules over the disc algebra are studied.The author relates extensions of these canonical modules to the symbol spaces of corresponding Hankel operators.In the context of function theory,an explicit formula of Ext(L^(2)_(a)(D),H^(2)(D))is obtained.Finally,it is also proved that Ext(L^(2)_(a)(D),L:(D))≠0.This may be the essential difference between the Hardy and the Bergman modules over the disk algebra.
基金Supported by National Natural Science Foundation of China,10101013
文摘In this paper the small Hankel operators on the Dirichlet-type spaces D p on the unit ball of C n are considered. A similar result to that of the one-dimensional setting is given, which characterizes the boundedness of the small Hankel operators on D p .
文摘The authors study the basic properties of Hankel operators and the structures of Hankel algebras relative to ordered groups,providing a new class of C*-algebras which are very useful in general C*-algebra theory.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971020)Doctoral Fund of Ministry of Education of China (RFDP)
文摘We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We furthermore obtain necessary and sufficient conditions for bounded Haplitz products HfTg-,where f∈L2（Bn,dvα） and g is a square integrable holomorphic function.
文摘Let S denote the class of functions that are analytic, normalized and univalent in the open unit disk E = {z: |z| S* and C respectively. A new subclass of analytic functions that generalize some known subclasses of analytic functions was defined and investigated. We obtained coefficient bounds, upper estimates for the Fekete-Szegö functional and the Hankel determinant.
基金Research partially supported by NNSF of China(11720101003)NSF of Guangdong Province(2018A030313512)+1 种基金Key projects of fundamental research in universities of Guangdong Province(2018KZDXM034)STU Scientific Research Foundation(NTF17009).
文摘We give a survey on the Berezin transform and its applications in operator theory. The focus is on the Bergman space of the unit disk and the Fock space of the complex plane. The Berezin transform is most effective and most successful in the study of Hankel and Toepltiz operators.
