Compactness estimates for the $\bar{\mathrm{\partial }}$ - Neumann problem in weighted $L^2$ - spaces

In this paper we discuss compactness estimates for the $\bar{\mathrm{\partial }}$-Neumann problem in the setting of weighted $L^2$-spaces on ${\mathbb{C}}^n\mathrm{.}$ For this purpose we use a version of the Rellich - Lemma for weighted Sobolev spaces.