On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces

Abstract

The article deals with the global Orlia-Morrey spaces GM ;'; (Rn). We find sufficient conditions on pairs of functions ('; ) and ( ; ), which ensure the boundedness of the fractional maximal operator M from GM ;'; (Rn) in GM ; ; (Rn). It is proved that under some additional conditions on the function ', the conditions obtained are also necessary. In the proof, the boundedness condition is essentially used, the maximal Hardy-Littlewood functions and the estimate of the norm of the characteristic function in global Orlicz-Morrey spaces are used.