Norm of Composition Operators From the Space of Exponential Cauchy Transforms to the Bloch-Type Space

Abstract

We calculate the norm of the composition operator from the space of the exponential Cauchy transforms to the Bloch-type space on the open unit disk in the complex plane in terms of the given symbols and defining functions, from which a characterization for the boundedness of the operator follows. The formula corrects a recent result in the literature, which is explained in detail. An interesting detailed analysis of the problem is conducted leading to a construction of a concrete counterexample.