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

TL;DR

This paper establishes a new criterion for the compactness of the $ar ext{-} ext{Neumann}$ operator on weighted $(0,q)$-forms in complex Euclidean spaces, advancing understanding in several complex variables.

Contribution

It introduces a novel characterization of compactness for the $ar ext{-} ext{Neumann}$ operator and provides a sufficient condition in weighted $L^2$-spaces on $ ext{C}^n$.

Findings

Derived a new criterion for compactness of the $ar ext{-} ext{Neumann}$ operator.

Established a sufficient condition for compactness in weighted $L^2$-spaces.

Enhanced understanding of the $ar ext{-} ext{Neumann}$ operator's properties in weighted complex spaces.

Abstract

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