The role of BMOA in the boundedness of weighted composition operators on the unit ball

We study the weighted composition operators W h,φ on Hardy space \(H^2 (\mathbb{B})\) whenever h ∈ BMOA (resp. h ∈ VMOA). Analogous results are given for \(H^p (\mathbb{B})\) 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).