Compactness of the $\bar{\mathrm{\partial }}$ - Neumann operator on weighted $(0,q)$- forms

As an application of a new characterization of compactness of the $\bar{\mathrm{\partial }}$-Neumann operator we derive a sufficient condition for compactness of the $\bar{\mathrm{\partial }}$- Neumann operator on $(0,q)$-forms in weighted $L^2$-spaces on ${\mathbb{C}}^n\mathrm{.}$