Boundedness for variable fractional integral operators and their commutators on Herz–Hardy spaces with variable exponent

Abstract

Let $Esubset mathbb{R}^{n}$ be a bounded open set. In this paper, we establish the boundedness of variable fractional integral operators and their commutators on variable Herz–Hardy spaces $Hdot{K}_{p(.)}^{alpha (.),q(.)}$ with three variable exponents by using the atomic decomposition.