Commutators of weighted Hardy operator on weighted $\lambda$-central Morrey space

TL;DR

This paper investigates the boundedness of commutators of the weighted Hardy operator on weighted $\,lambda$-central Morrey spaces and characterizes related Campanato spaces using new operators.

Contribution

It establishes the boundedness criteria for commutators on these spaces and introduces a new operator to characterize weighted $\,lambda$-central Campanato spaces.

Findings

Boundedness of commutators proved under doubling weight condition

Characterization of weighted $\,lambda$-central Campanato space achieved

New operator related to commutator introduced and analyzed

Abstract

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