Some Operators on GeneralizedWeighted Morrey Spaces over Quasi-Metric Measure Spaces

Abstract

In this paper we investigate the boundedness properties of the Hardy-Littlewood maximal operator and sublinear operators on generalized weighted Morrey spaces over quasi-metric measure spaces. The measure used is a doubling measure which satisfies the growth condition. The results showed that
the Hardy-Littlewood maximal operator was bounded from one generalized weighted Morrey spaces to another generalized weighted Morrey space over quasi-metric measure space with the same parameter under some conditions as well as the sublinear operator generated by Calder´on-Zygmund operator. The
results on the Hardy-Littlewood maximal operator are then applied to obtain the boundedness of the sublinear operators generated by generalized fractional integral from one generalized weighted Morrey spaces to another generalized weighted Morrey space with different parameters over quasi-metric measure
spaces either the Spanne type or Adams type. These results extend the known results on the operators.