Boundedness and Two-Weight Estimates for Fractional Hardy Operators and Their Commutators on Morrey–Herz Spaces

The principal objective of the present investigation is to rigorously establish the boundedness of fractional Hardy operators within the analytically intricate framework of two-weighted variable exponent Morrey–Herz spaces. As a technically demanding extension of these foundational results, analogous boundedness estimates are further derived for the associated commutator operators under the assumption that the symbol functions are members of the variable exponent bounded mean oscillation (BMO) space, thereby significantly broadening the applicability and analytical depth of the underlying operator-theoretic framework.