On the Weighted Boundedness of Fractional Rough Hardy Operators and Their Associated Commutators on Central Morrey Spaces

This paper investigates the boundedness of the fractional rough Hardy operator and its adjoint counterpart on weighted central Morrey spaces with variable exponents by combining the analytical framework of weighted variable exponent spaces with the structural properties of rough kernels, through which we establish a series of corresponding weighted norm estimates. Furthermore, by imposing the membership of the generating symbol in the variable exponent λ-central BMO space, we prove the boundedness of the associated commutator operators, thereby extending the existing boundedness theory for fractional Hardy-type operators and providing a unified framework for the analysis of rough operators and their commutators within weighted variable exponent function spaces.