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.