Reducing subspaces of multiplication operators on weighted Hardy spaces over bidisk

摘要

We consider weighted Hardy spaces over bidisk D~2 which generalize the weighted Bergman spaces A_α~2 (D~2). Let z, w be coordinate functions and M_(zN_wN) the multiplication by z~Nw~N for a natural number N. In this paper, we study the reducing subspaces of M_(zN_wN). In particular, we obtain the minimal reducing subspaces of M_(zw).