BMO and Hankel operators on Bergman spaces

Let BMO_∂^p be the space of functions on the open unit ball in Cⁿ with bounded mean oscillation in the Bergman metric defined using the volume L^P integral (see Introduction for precise definition). This paper studies the structure of BMO_∂^p. In particular, we show how BMO_∂^p depends on p. We also characterize BMO_∂^p in terms of certain Hankel operators acting on weighted Bergman L^P spaces. A parallel study is made on the companion space VMO_∂^p.