BMO and Hankel operators on Bergman space of the Siegel upper half-space

TL;DR

This paper investigates bounded and vanishing mean oscillation spaces on the Siegel upper half-space, using them to characterize bounded and compact Hankel operators on Bergman space, advancing understanding of operator theory in complex analysis.

Contribution

It introduces new characterizations of Hankel operators on Bergman space via mean oscillation spaces defined through the Berezin transform.

Findings

Characterization of bounded Hankel operators using mean oscillation spaces.

Criteria for compactness of Hankel operators on Bergman space.

Development of function space framework on Siegel upper half-space.

Abstract

On the setting of the Siegel upper half-space we study the spaces of bounded and vanishing mean oscillations which are defined in terms of the Berezin transform, and we use them to characterize bounded and compact Hankel operators on Bergman space.