Composition operators from the space of Cauchy transforms to Bloch and the little Bloch-type spaces on the unit disk
Abstract 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 ν as well as the little Bloch-type space B ν , 0 , consisting respectively of all holomorphic functions f on D such that sup z ∈ D ν ( z ) | f ′ ( z ) | ∞ , that is, of all holomorphic functions f on D such that lim | z | → 1 ν ( z ) | f ′ ( z ) | = 0 , for some weight function ν . As a byproduct of our results, norm of the operator is calculated when B ν is replaced by B ν / C .