The Boundedness for a Class of Rough Fractional Integral Operators on Variable Exponent Lebesgue Spaces

Abstract

In this paper, we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces, and establish their boundedness from $L^{p_1(\cdot)}(\mathbf{R}^n)$ to $L^{p_2(\cdot)}(\mathbf{R}^n)$.