Composition operators on QK spaces ✩

Suppose that φ is a nonconstant analytic self-map of the unit disk D. Compactness of composition operator Cφ between two Möbius spaces QK1 and QK2 is studied. Moreover, necessary and sufficient condition for Cφ from the Dirichlet space D to a general class of analytic functions F(p,q, s) to be compact is given in terms of the map φ. © 2006 Elsevier Inc. All rights reserved.