“…This question was asked by Rudin in his book [4, p.78] and it is still open. Recently, for n = 2, two types of important invariant subspaces known as inner-sequence based invariant subspaces and invariant subspaces generated by two inner functions have been extensively studied by various authors in different context(see [6,9,8,7,11,12]). In this paper, inspired from these studies, we define two new types of invariant subspaces of H 2 (D n ) by considering a larger class of functions than inner functions.…”