  Let $d\ge 1, \ell\in\Z^d$, $m\in \mathbb Z^+$ 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 Ratnakumar and Shrivastava \cite{RS1} Littlewood-Paley
square function $$T(f_1,\dots ,
f_m)(x)=\Big(\sum\limits_{\ell\in\Z^d}|\int_{\mathbb{R}^d}f_1(x-\theta_1
y)\cdots f_m(x-\theta_m y)e^{2\pi i \ell \cdot y}K (y)dy|^2\Big)^{1/2} $$ is
bounded from $L^{p_1}(\mathbb{R}^d) \times\cdots\times L^{p_m}(\mathbb{R}^d) $
to $L^p(\mathbb{R}^d) $ when $2\le p_i<\infty$ satisfy $1/p=1/p_1+\cdots+1/p_m$
and $1\le p<\infty$. Our proof is based on a modification of an inequality of
Guliyev and Nazirova \cite{GN} concerning multilinear convolutions.
