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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 Sobolevspaces.

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