Two-Weight Inequalities for Commutators of Fractional Integrals on Morrey Spaces

Abstract

In this article, via the relation between the higher order commutator            $I_{\alpha}^{b,m}$ and its sparse counterparts,
we establish two different types of the two-weight
boundedness of $I_{\alpha}^{b,m}$ on Morrey spaces.
The main novelties of these results include the predual
of the weighted Morrey space $L^{p,\lambda}(\sigma)$, $X^{p',\lambda}_\sigma(\mathbb{R}^n)$,
the boundedness of generalized fractional Orlicz maximal
operators on Morrey spaces and the boundedness of generalized Orlicz maximal
operators on $X^{p',\lambda}_\sigma(\mathbb{R}^n)$.