The role of BMOA in the boundedness of weighted composition operators

摘要

Boundedness (resp. compactness) of weighted composition operators W-h,W- phi acting on the classical Hardy space H-2 as W-h,W- phi f = h (f o phi) are characterized in terms of a Nevanlinna counting function associated to the symbols h and phi whenever h is an element of BMOA (resp. h is an element of VMOA). Analogous results are given for H-p spaces and the scale of weighted Bergman spaces. In the latter case, BMOA is replaced by the Bloch space (resp. VMOA by the little Bloch space). (C) 2010 Elsevier Inc. All rights reserved.