Toeplitz Operators On The Weighted Bergman Space Over The Bidisk

In this thesis, we mainly discuss the Bloch space and the Toeplitz operators defined on the weighted Bergman space on the bidisk. We define the Bloch space and the growth-type space and we prove that Bloch space is isomorphism to the dual space of weighted Bergman space. After that, we focus on the boundness and compactness of the Toeplitz operators. We take advantage of relations between weighted Bergman projection Pa Carleson measure, as well as the function theory of several complex variables.In chapter one, we list some related research background, giving some basic defini-tions and symbols.In chapter two, we discuss the Bloch space on the bidisk. We give the definition of the Bloch space and the growth-type space, then prove that the Bloch space is linearly homeomorphism to the dual space of the weighted Bergman space.In chapter three, we focus on the boundness and the compactness of the Toeplitz operators on the weighted Bergman space on the bidisk, we prove that if a complex Borel measure μ satisfies the condition (R), then Tμα is a bounded operator on the weighted Bergman space Lα1(dva) if and only if Q(μ)∈Ltlog2∞/t. Similarly, if a complex Borel measure μ satisfies the condition (R0),then Tμα is a compact operator on the weighted Bergman space if and only if Q(μ)∈Ltlog2/t∞,0...