Reducing subspaces of multiplication operators on weighted Hardy spaces over bidisk

Abstract

We consider weighted Hardy spaces over bidisk 𝔻² which generalize the weighted Bergman spaces A²_α(𝔻²). Let z,w be coordinate functions and M_z^Nw^N the multiplication by z^Nw^N for a natural number N. In this paper, we study the reducing subspaces of M_z^Nw^N. In particular, we obtain the minimal reducing subspaces of M_zw.