Compactness of Hankel Operators with Conjugate Holomorphic Symbols on Complete Reinhardt Domains in $\mathbb{C}^2$

TL;DR

This paper characterizes when Hankel operators with conjugate holomorphic symbols are compact on Bergman spaces over certain Reinhardt domains in complex two-dimensional space, extending understanding in complex analysis.

Contribution

It provides new characterizations of compact Hankel operators with conjugate holomorphic symbols on various classes of Reinhardt domains in rac{C}^2.

Findings

Characterization on bounded convex Reinhardt domains

Characterization on smooth bounded pseudoconvex Reinhardt domains

Extension of compactness criteria to broader domain classes

Abstract

In this paper we characterize compact Hankel operators with conjugate holomorphic symbols on the Bergman space of bounded convex Reinhardt domains in $\mathbb{C}^2$. We also characterize compactness of Hankel operators with conjugate holomorphic symbols on smooth bounded pseudoconvex complete Reinhardt domains in $\mathbb{C}^2$.