Norm of the general polynomial differentiation composition operator from the space of Cauchy transforms to the mth weighted-type space on the unit disk

Abstract

We introduce the general polynomial differentiation composition operator (Formula presented.) where (Formula presented.), (Formula presented.), (Formula presented.), are holomorphic functions on the open unit disk (Formula presented.) and (Formula presented.), (Formula presented.), are holomorphic self-maps of (Formula presented.), calculate norm of the operator acting from the space of Cauchy transforms to the (Formula presented.) th weighted-type space, and characterize its boundedness, as well as the boundedness of the operator acting from the space of Cauchy transforms to the little (Formula presented.) th weighted-type space.