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

TL;DR

This paper investigates compactness estimates for the ar-Neumann problem in weighted L^2 spaces on complex Euclidean space, utilizing a weighted Sobolev space Rellich-Lemma to advance understanding in several complex variables.

Contribution

It introduces a new approach using a weighted Sobolev space Rellich-Lemma to establish compactness estimates for the ar-Neumann problem in weighted L^2 spaces.

Findings

Established compactness estimates in weighted L^2 spaces

Applied a version of the Rellich-Lemma for weighted Sobolev spaces

Extended previous results to a weighted setting in complex analysis

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.