Multilinear Fourier multipliers on variable Lebesgue spaces
  In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem of multipliers on variable exponent Lebesgue spaces. Moreover, we present a Mihlin-H\"ormander type theorem for multilinear Fourier multipliers on weighted variable Lebesgue spaces and give some applications. 
Jineng Ren and Wenchang Sun
math.CA