Stein–Weiss inequalities on local Morrey spaces with variable exponents

Abstract

This paper establishes the Stein–Weiss inequalities on local Morrey spaces with variable exponents. It is presented as the boundedness of the fractional integral operators on power-weighted local Morrey spaces with variable exponents with different power weights. As a consequence of the main result, we obtain some Poincaré inequalities for local Morrey spaces with variable exponents.