Riesz potential in the local Morrey-Lorentz spaces and some applications

Abstract

In this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential I ? in the local Morrey-Lorentz spaces M p, q; ? loc ? (Rn). This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey-Lorentz spaces M p, q; ? loc ? (Rn). © 2018 Walter de Gruyter GmbH, Berlin/Boston.