Composition operators from the space of Cauchy transforms to Bloch and the little Bloch-type spaces on the unit disk

We completely characterize the boundedness and compactness of composition operators from the space of Cauchy transforms on the unit disk D, into the Bloch-type space B-v as well as the little Bloch-type space B-v,B-0, consisting respectively of all holomorphic functions f on D such that sup(z is an element of D) v(z)vertical bar f'(z) < infinity, that is, of all holomorphic functions f on D such that lim(vertical bar z vertical bar -> 1) v(z)vertical bar f '(z)vertical bar = 0, for some weight function m. As a byproduct of our results, norm of the operator is calculated when B-v is replaced by B-v/C. (C) 2011 Elsevier Inc. All rights reserved.