Composition Operators from the Bloch Space into the Spaces Qt

Suppose that ϕ(z) is an analytic self-map of the unit disk ∆. We consider the boundedness of the composition operator C ϕ from Bloch space Ꮾ into the spaces Q T (Q T ,0) defined by a nonnegative, nondecreasing function T (r) on 0 ≤ r < ∞. 1. Introduction. Let ∆ = {z : |z| < 1} be the unit disk of complex plane C and let H(∆) be the space of all analytic functions in ∆. For a ∈ ∆, Green's function with logarithmic singularity at a ∈ ∆ is denoted by g(z, a) = log |(1 − ¯ az)/ (a − z)|. For 0 < p < ∞, the space Q p consists of all functions f analytic in ∆ for which