Composition-Differentiation Operator on the Bergman Space

Abstract

We investigate the properties of composition-differentiation operator Dψ on the Bergman space of the unit disk L2a(D). Specifically, we characterize the properties of the reproducing kernel for the derivatives of the Bergman space functions. Moreover, we determine the adjoint properties of Dψ whenever ψ is self analytic map of the unit disk D.