Some Conditions for the Boundedness of Commutators of Fractional Integrals on Generalized Weighted Morrey Spaces

Abstract

In this paper, we investigate the boundedness of commutators generated by $b\in BMO$ and fractional integrals $I_\alpha$ from $\mathcal{M}_{\psi_1}^{p,w^p}$ to $\mathcal{M}_{\psi_2}^{q,w^q}$ for $1<p<q<\infty$. We obtain some new conditions for the pair $(\psi_1,\psi_2)$ of the functions $\psi_1$ and $\psi_2$ on $\mathbb{R}^n\times (0,\infty)$ that ensure the boundedness properties.