The characterization of the weighted modified Morrey spaces

In this study, firstly we define the weighted modified Morrey spaces ? Lp,?(Rn, ?) for the weight function ? in the class Ap(Rn) and we prove the boundedness of some classical operators as the generalized fractional maximal operator M? and the generalized fractional integral operator I? from the weighted modified Morrey spaces ? Lp,?(Rn, ?p) to ? Lq,?(Rn, ?q) with ?q ? A1+q/p?(Rn) and from ? L1,?(Rn, ?) to weighted weak modified Morrey spaces WeLq,?(Rn, ?q), with ? ? A1,q(Rn) by proving the appropriate weighted norm inequalities.