Dominant sets for model spaces in several variables

Let $I$ be an inner function in $\mathcal{D}=B_{n_1}\times B_{n_2}\cdots \times B_{n_k}$, where $B_n$ denotes the open unit ball of ${\mathbb{C}}^n$, $n\ge 1$. We construct dominant sets for the space $H^2\ominus I{H}^2$, where $H^2=H^2(\mathcal{D})$ denotes the standard Hardy space.