In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators t...In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same.Also,some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.展开更多
In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere.As a consequence,man...In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere.As a consequence,many non-trivial examples of(semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.展开更多
There is a singular integral operators Sj on the Fock space F2(C),which originated from the unitarily equivalent version of the Hilbert transform on L2(R).In this paper,we give an analytic characterization of function...There is a singular integral operators Sj on the Fock space F2(C),which originated from the unitarily equivalent version of the Hilbert transform on L2(R).In this paper,we give an analytic characterization of functions j with finite zeros such that the integral operator Sj is bounded on F2(C)using Hadamard’s factorization theorem.As an application,we obtain a complete characterization for such symbol functions j such that the Berezin transform of Sj is bounded while the operator Sj is not.Also,the corresponding problem in higher dimensions is considered.展开更多
基金supported in part by the National Natural Science Foundation of China(11201331,11771323)。
文摘In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same.Also,some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.
基金supported by the National Natural Science Foundation of China(Nos.11201331,11771323).
文摘In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere.As a consequence,many non-trivial examples of(semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.
基金supported in part by the Natural Science Foundation of Tianjin City of China(Grant No.19JCQNJC14700).
文摘There is a singular integral operators Sj on the Fock space F2(C),which originated from the unitarily equivalent version of the Hilbert transform on L2(R).In this paper,we give an analytic characterization of functions j with finite zeros such that the integral operator Sj is bounded on F2(C)using Hadamard’s factorization theorem.As an application,we obtain a complete characterization for such symbol functions j such that the Berezin transform of Sj is bounded while the operator Sj is not.Also,the corresponding problem in higher dimensions is considered.
