Two-Weighted Estimate for Generalized Fractional Integral and Its Commutator on Generalized Fractional Morrey Spaces

Abstract

The aim of this paper is to establish the mapping properties of generalized fractional integral $I_ρ$ and its commutator $[b,I_ρ]$ formed by $b∈{\rm BMO}(\mathbb{R}^n)$ and the $I_ρ$ on generalized fractional weighted Morrey spaces $\mathcal{L}^{p,η,φ}_ω (\mathbb{R}^n),$ where $φ$ is a positive and non-decreasing function defined on $(0,∞),$ $η∈(0,n)$ and $p∈[1, \frac{n}{η}).$