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 $r ≤ 1$ for which these operators map products of Lebesgue spaces $L^p(\mathbbR^n)$ into the Hardy spaces $H^r(\mathbbR^n)$. 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.