Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk

Abstract

In this paper, we study the invariant subspace and reducing subspace of the weighted Bergman space over bidisk. The minimal reducing subspace of Toeplitz operator $$T_{z^N}=T_{z_1^N{z}_2^N}$$ is completely described, and Beurling-type theorem of some invariant subspace of the weighted Bergman space over bidisk is also obtained.