Weighted BMO and Hankel operators between Bergman spaces

TL;DR

This paper introduces weighted BMO and VMO spaces on the unit ball to characterize bounded and compact Hankel operators between Bergman spaces, solving longstanding open problems in the field.

Contribution

It provides a new framework for understanding Hankel operators using weighted BMO/VMO spaces, addressing open questions from past research.

Findings

Characterization of bounded Hankel operators using weighted BMO spaces.

Criteria for compactness of Hankel operators via weighted VMO spaces.

Resolution of two open problems from Janson (1988) and Wallsten (1990).

Abstract

We introduce a family of weighted BMO and VMO spaces for the unit ball and use them to characterize bounded and compact Hankel operators between different Bergman spaces. In particular, we resolve two problems left open by S. Janson in 1988 and R. Wallsten in 1990.