N_ψ-Type Quotient Modules in H^2(D^n)

In this paper, N ψ -type quotient modules H 2 (D n )/K of the Hardy module on polydisc are defined, where K is the submodule generated by {z 1 -ψ (z k ); 2 [[EQUATION]] k [[EQUATION]] N} for a finite Blaschke product ψ . The alternative characterizations are given and an orthonormal basis is constructed. Then we show that the self-commutators and cross-commutators are in trace class, self commutators are Hilbert-Schmidt. Moreover, the traces and the Hilbert-Schmidtness norms are given respectively.