Composition operators on Q(P) spaces

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