Functions of bounded mean oscillation and Hankel operators on compact abelian groups

TL;DR

This paper extends the theory of functions of bounded mean oscillation and Hankel operators to compact abelian groups with linearly ordered duals, characterizing these spaces via Hankel operator boundedness.

Contribution

It introduces a generalization of BMO functions and Hankel operators to a broader class of groups, providing new characterizations in this setting.

Findings

Characterization of BMO spaces on compact abelian groups with ordered duals.

Boundedness criteria for Hankel operators on these groups.

Extension of classical harmonic analysis concepts to new algebraic structures.

Abstract

Generalization of functions of bounded mean oscillation and Hankel operators to the case of compact abelian groups with linearly ordered dual is considered. Spaces of functions of bounded mean oscillation and of bounded mean oscillation of analytic type on such groups are described in terms of boundedness of corresponding Hankel operators under the assumption that the dual group contains a minimal positive element.