Abstract: By using hierarchical decomposition of function and the weighted inequalities, and by means of the boundedness of Hardy operator on variable Lebesgue spaces and the properties of bounded mean oscillation function space (BMO) functions, the author gave the boundedness of the higher order commutators generated by fractional Hardy operators with variable index and BMO functions on weighted HerzMorrey spaces with variable exponent.

Key words: variable index, fractional Hardy operator, Ap(·) weight, BMO functions, HerzMorrey space