Analysis on the Intersection of Pseudoconvex Domains

TL;DR

This paper examines how key analytic operators like the ar-Neumann, Bergman projection, and Hankel operators behave when applied to the intersection of pseudoconvex domains, highlighting their preservation of properties.

Contribution

It provides new insights into the preservation of analytic properties of these operators on intersected pseudoconvex domains.

Findings

Analytic properties are preserved under intersection.

Behavior of ar-Neumann operator on intersected domains.

Stability of Bergman and Hankel operators in intersections.

Abstract

In this note, we discuss the preservation of certain analytic properties of the $\overline{\partial}$-Neumann operator, Bergman projection and Hankel operators on the intersection of pseudoconvex domains.