Let R(D) be the algebra generated in Sobolev space W 22(D) by the rational functions with poles outside the unit disk $ \overline D $ . In this paper the multiplication operators M g on R(D) is studied and it is proved that M g ～ $ M_{z^n } $ if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then M g has uncountably many Banach reducing subspaces if and only if n > 1.
In this paper, we study the invariant subspaces of the operator Mz on the Sobolev disk algebra R（D） and characterize the invariant subspace with finite codimension.
