Composition operators from logarithmic Bloch spaces to Bloch-type spaces

In this paper, we characterize the analytic self-maps phi of the unit disk D in C that induce continuous and compact composition operators C-phi from the logarithmic Bloch spaces, introduced by Stevic [12], into the mu-Bloch space, where mu is any weight defined on D. We give characterizations in terms of quotients of the logarithmic Bloch norm of the n-th power of phi and the mu-Bloch norm of the n-th power of the identity function I on D. This solves partially the problem proposed by Zhao [20].