Boundedness and compactness of Hankel operators on the sphere

We consider Hankel operators on the Hardy space of the unit sphere in Cn. We show that a large amount of information about the function f − Pf can be recovered from the Hankel operator Hf . For example, if Hf is compact, then the function f −Pf is necessarily in VMO. © 2008 Elsevier Inc. All rights reserved