Norm of difference of general polynomial weighted differentiation composition operators from Cauchy transform spaces into derivative Hardy spaces

Abstract

‎In this paper‎, ‎we investigated boundedness of difference of general polynomial weighted differentiation composition operators from Cauchy transform spaces into function spaces $S=\{f:\ \ f'\in H^1\}$ and $S^2=\{f:\ \ f'\in H^2\}$ with derivative in Hardy spaces‎. ‎‎‎We also obtained an exact formula for the norm of this operator and prove that there is no composition isometry from the Cauchy transform spaces into $S$ and $S^2$ ‎spaces.‎