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

Generalizations of the notions of function of bounded mean oscillation and Hankel operator to the case of compact abelian groups with linearly ordered dual group 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 the boundedness of corresponding Hankel operators under the assumption that the dual group contains a minimal positive element.