Compactness estimates for the $\overline \partial $ - Neumann problem in weighted $L^2$ - spaces

Abstract

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