Reducing Subspaces For A Class Of Analytic Toeplitz Operators Of Weighted Hardy Spaces Over The Bidisk

In this thesis,we study the reducing subspaces for a class of analytic Toeplitz operator of the weighted Hardy space H2(βα,D2)over bidisk D2.The thesis is organized as follows:In Chapter 1,we discuss some related research background of our study and give some basic concepts and symbols.Finally,we show some basic results on reducing sub-spaces.In Chapter 2,we study the reducing subspaces of TzN on the weighted Hardy spaces H2(βα,D).And we give the complete characterization of the nontrivial reducing subspaces of TzN in the case N = 2 or N>2.In Chapter 3,we discuss the restriction of TzN on its reducing subspaces is similar to the sum of N copies of the Bergman shift.In Chapter 4,we describe the reducing subspaces of Toeplitz operator Tz1N(T2N2)on the weighted Hardy spaces H2(βα,D2)over bidisk D2.In Chapter 5,we describe the reducing subspaces of Toeplitz operator Tz1z2 on the weighted Hardy spaces H2(βα,D2)over bidisk D2.