Certain Multi(sub)linear square functions

Loukas Grafakos, Sha He, Qingying Xue

Let $d\ge 1,\ell \in {\mathbb{Z}}^d$, $m\in {\mathbb{Z}}^{+}$ and ${\theta }_i$, $i=1,\dots ,m$ are fixed, distinct and nonzero real numbers. We show that the $m$-(sub)linear version below of the Ratnakum…