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
In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condit...In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condition on the symbols to guarantee TfHg = HgTf.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 introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras,including the study of boundedness,compactness,Fredholm property,index theory,spectrum...In this paper,we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras,including the study of boundedness,compactness,Fredholm property,index theory,spectrum and essential spectrum,norm and essential norm,Schatten-p classes,and the C^(∗) algebras generated by them.展开更多
This paper gives the necessary and sufficient conditions for Toeplitz operator or Hankel operator of L~∞-symbol being compact on the weighted Bergman space of the unit ball in C^n.
The authors give some new necessary conditions for the boundedness of Toeplitz products Tf^aTg^a on the weighted Bergman space Aa^2 of the unit ball, where f and g are analytic on the unit ball. Hankel products HfH9^...The authors give some new necessary conditions for the boundedness of Toeplitz products Tf^aTg^a on the weighted Bergman space Aa^2 of the unit ball, where f and g are analytic on the unit ball. Hankel products HfH9^＋ on the weighted Bergman space of the unit ball are studied, and the results analogous to those Stroethoff and Zheng obtained in the setting of unit disk are proved.展开更多
In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞（D）, and then that a semicommutator of two Toeplitz operators on the Dirich...In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞（D）, and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact. We also prove that a dual Hankel operator Re with φ ∈ W^1,∞（D） is of finite rank if and only if Be is orthogonal to the Dirichlet space for some finite Blaschke product B, and give a sufficient and necessary condition for the semicommutator of two dual Toeplitz operators to be of finite rank.展开更多
In this paper,we generalize the concept of asymptotic Hankel operators on H2(D)to the Hardy space H2(Dn)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some propert...In this paper,we generalize the concept of asymptotic Hankel operators on H2(D)to the Hardy space H2(Dn)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence.Meanwhile,we introduce ith-partial Hankel operators on H2(Dn)and obtain a characterization of its compactness for n>1.Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn).It is also shown that a Toeplitz operator with symbolφis asymptotic Hankel if and only if φ is holomorphic function in L∞(Tn).展开更多
This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic ...This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.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.
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)).
基金Supported by the National Natural Science Foundation of China (Grant Nos.10671028 10971020)
文摘In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condition on the symbols to guarantee TfHg = HgTf.
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G.Cao was supported by the NNSF of China(Grant No.12071155)L.He was supported by the NNSF of China(Grant No.11871170).
文摘In this paper,we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras,including the study of boundedness,compactness,Fredholm property,index theory,spectrum and essential spectrum,norm and essential norm,Schatten-p classes,and the C^(∗) algebras generated by them.
基金Project supported by the Doctoral Program Foundation of Institute of Higher Education, PRC.
文摘This paper gives the necessary and sufficient conditions for Toeplitz operator or Hankel operator of L~∞-symbol being compact on the weighted Bergman space of the unit ball in C^n.
基金supported by the National Natural Science Foundation of China (No.10671028).
文摘The authors give some new necessary conditions for the boundedness of Toeplitz products Tf^aTg^a on the weighted Bergman space Aa^2 of the unit ball, where f and g are analytic on the unit ball. Hankel products HfH9^＋ on the weighted Bergman space of the unit ball are studied, and the results analogous to those Stroethoff and Zheng obtained in the setting of unit disk are proved.
基金supported by National Natural Science Foundation of China (Grant Nos.10971195 and 10771064)Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090689 and Y6110260)Zhejiang Innovation Project (Grant No. T200905)
文摘In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞（D）, and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact. We also prove that a dual Hankel operator Re with φ ∈ W^1,∞（D） is of finite rank if and only if Be is orthogonal to the Dirichlet space for some finite Blaschke product B, and give a sufficient and necessary condition for the semicommutator of two dual Toeplitz operators to be of finite rank.
基金Support of UGC Research Grant [Ref.No.:21/12/2014(ii)EU-V,Sr.No.2121440601] to second author for carrying out the research work is gratefully acknowledged
文摘In this paper,we generalize the concept of asymptotic Hankel operators on H2(D)to the Hardy space H2(Dn)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence.Meanwhile,we introduce ith-partial Hankel operators on H2(Dn)and obtain a characterization of its compactness for n>1.Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn).It is also shown that a Toeplitz operator with symbolφis asymptotic Hankel if and only if φ is holomorphic function in L∞(Tn).
基金supported by CSIR,New Delhi(Grant No.25(240)/15/EMR-Ⅱ)
文摘This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.
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.
