Stein–Weiss inequalities on Herz spaces with variable exponent

This paper extends the celebrated Stein–Weiss inequalities to the Herz spaces with variable exponents. It is an extension of the classical Stein–Weiss inequalities and the Stein–Weiss inequalities on Lebesgue spaces with variable exponents. The Stein–Weiss inequalities to the Herz spaces with variable exponents are presented as the boundedness of the fractional integral operators on the power weighted Herz spaces with variable exponents.