Trilinear Fourier multipliers on Hardy spaces

In this paper, we obtain the $H^{p_1}\times H^{p_2}\times H^{p_3}\to H^p$ boundedness for trilinear Fourier multiplier operators, which is a trilinear analogue of the multiplier theorem of Calder\'on and Torchinsky (Adv. Math. 24 : 101-171, 1977). Our result improves the trilinear estimate in the very recent work of the authors, Lee, Heo, Hong, Park, and Yang (Math. Ann., to appear ) by additionally assuming an appropriate vanishing moment condition, which is natural in the boundedness into the Hardy space $H^p$ for $0<p\le 1$.