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

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