Differentiability and holder continuity of riesz potentials of orlicz functions

Abstract

Our aim in this paper is to discuss differentiability properties of Riesz potentials Raf of functions / in generalized Lp(Rn) spaces. In fact, we show that if / belongs to a certain Orlicz class, then Raf has partial derivatives of order i which satisfy Hölder type condition. © 2000, Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München. All rights reserved.