Toeplitz Operators And Hankel Operators On Some Analytic Function Spaces

In this paper,we study the complex symmetric Toeplitz operator on Fock space F² and harmonic Fock space F_h²,Toeplitz operator on the vector-valued exponential weight function Bergman space,and the big Hankel operator on the regular weighted harmonic Bergman space.Firstly,we study the necessary and sufficient conditions for Toeplitz operator to be a complex symmetric operator on the conjugate operator C_?,? on F² or F_h².It is proved that Toeplitz operator is a complex symmetric operator with respect to conjugate C_?,? on F² and F_h².Secondly,by using carleson condition and mean value function,the necessary and sufficient conditions for the sign of positive operator value function Toeplitz op-erator to be bounded and compact on A_?²(H) are obtained.Finally,we obtain the equivalent conditions of boundedness and compactness of big Hankel operators on the sign of radial functions on the regular weighted harmonic Bergman space h_?²(D).