The Problem Of Reducing Subspaces For A Class Of Reproducing Kernel Spaces

In this paper, first we introduce some results of the reducing subspaces of weighted shift operators andweighted Bergman space over unit polydisc respectively. Then we study the reducing subspaces of a classof reproducing kernel spaces, and a complete classification of the minimal reducing subspaces of weightedunilateral shift operators of finite multiplicity on this class of reproducing kernel spaces is obtained.