Hilbert-Schmidt Norms of Self-Commutator and Cross-Commutator on $N_{\eta }$-type Quotient Modules in Polydisc

Anjian Xu, Yuchao Xiang

Let ${\eta }_1,\cdots ,{\eta }_d$ be nonconstant one-variable inner functions satisfying ${\eta }_i(0)=0$ for all $1\le i\le d$. Denote by $M_{\eta }$ the submodule of the Hardy space $H^{2}(\mathb…