Obstructions for Compactness of Hankel Operators: Compactness Multipliers

TL;DR

This paper explores the relationship between the compactness of Hankel operators and the geometry of domains, introducing and generalizing the concept of compactness multipliers to generate compact Hankel operators.

Contribution

It establishes that compactness multipliers induce compact Hankel operators and generalizes this concept to vector fields and matrices.

Findings

Compactness multipliers induce compact Hankel operators

Generalization of compactness multipliers to vector fields and matrices

Provides a geometric perspective on Hankel operator compactness

Abstract

We establish a connection between compactness of Hankel operators and geometry of the underlying domain through compactness multipliers for the $\overline{\partial}$-Neumann operator. In particular, we prove that any compactness multiplier induces a compact Hankel operator. We also generalize the notion of compactness multipliers to vector fields and matrices and then we use this generalization to generate compact Hankel operators.