Young's inequality for convolution of functions states that for $f\in L^p(\mathbb{R}^d)$ and $g\in L^q(\mathbb{R}^d)$ we have
$\|f\star g\|_r\le\|f\|_p\|g\|_q$
for $p$, $q$, $r$ satisfying
$\frac{1}{p}+\frac{1}{q}=\frac{1}{r}+1.$
Does this inequality hold for sequences? That is, can we replace $L^n(\mathbb{R}^d)$ with $\ell_n$, $n=p,q$ respectively, where convolution of sequences is the discrete convolution?