Persson, Lars-ErikSamko, Natasha2018-12-072018-12-072011-050022-247X1096-0813http://hdl.handle.net/10400.1/11731We study the weighted p -> q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces L-p.phi(R-n, w) defined by an almost increasing function phi(r) and radial type weight w(vertical bar x vertical bar). We obtain sufficient conditions, in terms of some integral inequalities imposed on phi and w, for such a p -> q-boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p -> q-boundedness of the Riesz potential operator. (c) 2010 Elsevier Inc. All rights reserved.engSingular integral-operatorsFractional integralsMaximal operatorSufficient conditionsVariable exponentRiesz-potentialsBoundednessjournal article10.1016/j.jmaa.2010.11.029