A Study On The Invariant Decomposition Of Quotient Submodules In A Bidisk Hardy Space

For the classical Hardy space with one variable,we can get the form of invariant subspace by the Beurling theorem.But for the bidisk of the Hardy space is more complex,so we can start with some relatively simple concrete submodules,so as to have a better understanding of the general situation.In this paper,we study two special submodules:inner sequence based invariant submodule M=(?)?j=0 qjH2(z)?j and two inner sequences based invariant submodule M=??j=0?j(z)H2(z)(?)(?j(?)H2(?)(?)?j+1(w)H2(?)).We study that under what conditions do their corresponding quotient submodules have invariant decomposition.