  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.
