Abstract:
The definitions and some basic properties of the variable exponent Lebesgue space are mentioned. Then, by the properties of weighted Lebesgue spaces with variable exponents and the boundedness of the multilinear fractional integral operator on
Lp, based on the definition of the weighted Herz spaces with variable exponent, using the real methods in harmonic analysis, the boundedness of the multilinear fractional integral operators on the product weighted Herz spaces with variable exponents is obtained.