The role of BMOA in the boundedness of weighted composition operators ✩

Boundedness (resp. compactness) of weighted composition operators Wh,ϕ acting on the classical Hardy space H2 as Wh,ϕf = h(f ◦ ϕ) are characterized in terms of a Nevanlinna counting function associated to the symbols h and ϕ whenever h ∈ BMOA (resp. h ∈ VMOA). Analogous results are given for Hp 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). © 2010 Elsevier Inc. All rights reserved