On the boundedness of multilinear Fourier multipliers on Hardy spaces

Abstract

In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. In particular, we prove that the multilinear Fourier multiplier operator of Hörmander type is bounded from H p 1 × • • • × H pm to H p for 0 < p1, . . . , pm ≤ 1 with 1/p1 + • • • 1/pm = 1/p, under suitable cancellation conditions. As a result, we extend the trilinear estimates in [17] to general multilinear ones and improve the boundedness result in [18] in limiting situations.