Integrability of Mean Oscillation with Applications to Hankel Operators

摘要

We introduce and study a family of Banach spaces IMOps,sigma of functions on the open unit ball Bn in Cn, defined by an integrability condition of the mean oscillation in the Bergman metric. Our main results include a decomposition theorem for IMOps,sigma, a characterization of holomorphic functions in IMOps,sigma, and an application of IMOps,sigma to the boundedness and compactness of Hankel operators between weighted Bergman spaces.