Commutators of weighted Hardy operator on weighted $\hat{I}»$-central Morrey space

Abstract

In this paper, the authors prove the boundedness of commutators generated by the weighted Hardy operator on weighted $\hat{I}»$-central Morrey space with the weight $\ddot{I}‰$ satisfying the doubling condition. Moreover, the authors give the characterization for the weighted $\hat{I}»$-central Campanato space by introducing a new kind of operator which is related to the commutator of weighted Hardy operator.