  The Orlicz $\left( \ell_{2},\ell_{1}\right) $-mixed inequality states that $$
\left( \sum_{j_{1}=1}^{n}\left( \sum_{j_{2}=1}^{n}\left\vert A(e_{j_{1}
},e_{j_{2}})\right\vert \right) ^{2}\right) ^{\frac{1}{2}}\leq\sqrt
{2}\left\Vert A\right\Vert $$ for all bilinear forms
$A:\mathbb{K}^{n}\times\mathbb{K}^{n}\rightarrow \mathbb{K}$ and all positive
integers $n$, where $\mathbb{K}^{n}$ denotes $\mathbb{R}^{n}$ or
$\mathbb{C}^{n}$ endowed with the supremum norm. In this paper we extend this
inequality to multilinear forms, with $\mathbb{K}^{n}$ endowed with $\ell_{p}$
norms for all $p\in\lbrack1,\infty].$
