On closed range for $\bar{\partial}$

TL;DR

This paper provides a sufficient condition ensuring the ar operator has a closed range on pseudoconvex domains in complex space, which may be unbounded, advancing understanding of complex analysis and partial differential equations.

Contribution

It introduces a new sufficient condition for the closed range property of the ar operator on pseudoconvex domains, including unbounded cases.

Findings

Established a sufficient condition for ar closed range

Applicable to unbounded pseudoconvex domains

Enhances understanding of ar operator properties

Abstract

A sufficient condition for $\bar{\partial}$ to have closed range is given for pseudoconvex, possibly unbounded domains in $\mathbb{C}^n$.