  In this article, we present some results about Fourier multipliers on Hardy
spaces in the product case. We mainly give descriptions of multipliers from the
space $H^1(\mathbb{T}\times\mathbb{T})$ into the space $\ell^2$ and from the
space $H^1(\mathbb{R}_+^2\times\mathbb{R}_+^2)$ into the space $L^1$.
