BMO and Hankel operators on Bergman spaces

Kehe Zhu

Vol. 155 (1992), No. 2, 377–395

DOI: 10.2140/pjm.1992.155.377

Abstract

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 V MO_∂^p.

Mathematical Subject Classification 2000

Primary: 47B35

Secondary: 32A37, 46E15, 47B10

Milestones

Received: 30 July 1990

Revised: 15 April 1991

Published: 1 October 1992