On fractional deviation operators

Abstract

The so called fractional deviation operators are introduced. This class of integral transforms appears naturally from the study of iteration of fractional integrals of Riemann-Liouville type. Since B. Ross' formulation on fractional iteration process, among other problems selected by T. Osler [5] toward 1974, several authors have been working on this subject. In particular, are worth mentioning contributions of B. Rubin [7] that allowed an intrinsic connection between fractional integrals with different limits of integration (Love's question, see [5] also) and the corresponding Ross' problem for Chen fractional integrals, handled by A. Nahushev [4] and M. Salahitdinov, with broad applications to non local boundary value problems. In this article we consider deviation operators as integral transforms, their connection with operators of Rubin type and mapping properties between classical and weighted Lebesgue spaces.