Title: A multiplier inclusion theorem on product domains,
Abstract: In this note it is shown that the class of all multipliers from the
$d$-parameter Hardy space $H^1_{\mathrm{prod}} (\mathbb{T}^d)$ to $L^2
(\mathbb{T}^d)$ is properly contained in the class of all multipliers from $L
\log^{d/2} L (\mathbb{T}^d)$ to $L^2(\mathbb{T}^d)$.