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Journal of Function Spaces and Applications
Volume 6, Issue 1, Pages 88-104
http://dx.doi.org/10.1155/2008/383496

Composition operators from α to QK type spaces

Department of Mathematics and Physics, Anhui University of Science and Technology, Anhui, Huainan 232001, China

Received 1 February 2007

Academic Editor: Miroslav Englis

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Suppose that ϕ is an analytic self-map of the unit disk Δ. Necessary and sufficient condition are given for the composition operator Cϕf=fοϕ to be bounded and compact from α-Bloch spaces to QK type spaces which are defined by a nonnegative, nondecreasing function k(r) for 0r<. Moreover, the compactness of composition operator Cϕ from 0 to QK type spaces are studied, where 0 is the space of analytic functions of f with fH and f0=|f(0)|+f.