Composition operators on QP spaces

A holomorphic map phi of the unit disk into itself induces an operator C-phi on holomorphic functions by composition. We characterize bounded and compact composition operators C-phi on Q(p) spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of C-phi from analytic function space X to Q(p) spaces, X = Dirichlet space D, Bloch space B or B-0 = {f : f ' is an element of H-infinity}.