Differentiation and integration operators on weighted Banach spaces of holomorphic functions

We obtain a new natural description of the class of radial weights for which some previous results of A. Harutyunyan and W. Lusky concerning the boundedness of differentiation and integration operators on corresponding spaces are valid. To do this, we develop an elementary approach which is essentially different from the previous one and allows us to establish several new results and new characterizations of some popular classes of radial weights.