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September 10, 2025Open Access

The characterization of the weighted modified Morrey spaces

Key Points

The study defines weighted modified Morrey spaces and proves the boundedness of operators in these spaces.
Key findings show the generalized fractional maximal operator and integral operator maintain boundedness in weighted spaces.
Appropriate weighted norm inequalities are established, linking different Morrey space types and their properties.
These results enhance understanding of operator behavior in weighted modified Morrey spaces.

Abstract

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.

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