On Some Applications of a Special Integrodifferential Operators

Abstract

Let be a Banach space of complex-valued functions that are continuous on , where is the unit disc in the complex plane , and have th partial derivatives in which can be extended to functions continuous on , and let denote the subspace of functions in which are analytic in (i.e., ). The double integration operator is defined in by the formula . By using the method of Duhamel product for the functions in two variables, we describe the commutant of the restricted operator , where is an invariant subspace of , and study its properties. We also study invertibility of the elements in with respect to the Duhamel product.