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 \({H^{{p_1}}} \times \cdots \times {H^{{p_m}}}\) to Hp 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.

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