Hankel Operators on the Bergman spaces of Reinhardt Domains and Foliations of Analytic Disks

TL;DR

This paper investigates the boundary structure of pseudoconvex Reinhardt domains in complex two-space and establishes a compactness result for Hankel operators on their Bergman spaces, enhancing understanding of operator behavior in complex analysis.

Contribution

It provides new insights into the boundary analytic structure of Reinhardt domains and proves a compactness theorem for Hankel operators on their Bergman spaces.

Findings

Boundary analytic structure characterized

Compactness of Hankel operators established

Enhanced understanding of operator behavior in complex domains

Abstract

Let $\Omega\subset \mathbb{C}^2$ be a bounded pseudoconvex complete Reinhardt domain with a smooth boundary. We study the behavior of analytic structure in the boundary of $\Omega$ and obtain a compactness result for Hankel operators on the Bergman space of $\Omega$.