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.