BMOand Hankel operators on Bergman spaces

Abstract

Let BMO(partial derivative)p be the space of functions on the open unit ball in C(n) 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(partial derivative)p. In particular, we show how BMO(partial derivative)p depends on p. We also characterize BMO(partial derivative)p in terms of certain Hankel operators acting on weighted Bergman L(p) spaces. A parallel study is made on the companion space VMO(partial derivative)p.