Hardy Space Estimates for Multilinear Operators, II

Abstract

We continue the study of multilinear operators given by products of finite vectors of Calderón–Zygmund operators. We determine the set of all $r\le 1$ for which these operators map products of Lebesgue spaces $L^p({\mathbb{R}}^n)$ into the Hardy spaces $H^r({\mathbb{R}}^n)$. At the endpoint case $r=n/(n+m+1)$, where $m$ is the highest vanishing moment of the multilinear operator, we prove a weak type result.