Hormander’s Condition for Multilinear Fourier Multipliers

ABSTRACT: Let m be a positive integer. In this talk, we will introduce optimal conditions, expressed in terms of Sobolev spaces, on m-linear Fourier multiplier operators to be bounded from a product of Lebesgue or Hardy spaces to Lebesgue spaces. Our results are sharp and cover the bilinear case (m = 2) obtained by Miyachi and Tomita [1].