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 $H_{\mathrm{prod}}^1({\mathbb{T}}^d)$ 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 $L^2({\mathbb{T}}^d)$.

arXiv comment13 pages