Norm and Compactness of a Polynomial Differentiation Composition Operator on the Unit Disc

ABSTRACT The boundedness of the polynomial differentiation composition operator from the space of Cauchy transforms to the weighted Bergman space on the open unit disk is characterized in terms of the operator symbols and parameters, and some of the quantities and parameters appearing in the definitions of the spaces. Moreover, the norm of the operator is calculated in terms of them. Besides this, some necessary and sufficient conditions for the compactness of the operator are given.