The regularity of projection operators and solution operators to $\overline{\partial}$ on weakly pseudoconvex domains

TL;DR

This paper explores the relationship between the regularity of solution operators for the ar problem and projection operators onto the kernel of ar on weakly pseudoconvex domains, advancing understanding of complex analysis in these settings.

Contribution

It establishes a connection between the regularity of ar solution operators and projection operators, providing new insights into their interplay on weakly pseudoconvex domains.

Findings

Regularity of solution operators is linked to the existence of projection operators.

Provides conditions under which solution operators are regular.

Enhances understanding of ar problem solutions on weakly pseudoconvex domains.

Abstract

We relate the existence and regularity of a solution operator to on smoothly bounded pseudoconvex domains to the existence and regularity of a projection operator onto the kernel of dbar.