  In this note we prove that the discrete Riesz potential $I_{\alpha}$ defined
on $\mathbb{Z}^n$ is a bounded operator $H^p (\mathbb{Z}^n) \to \ell^q
(\mathbb{Z}^n)$ for $0 < p \leq 1$ and $\frac{1}{q} = \frac{1}{p} -
\frac{\alpha}{n}$, where $0 < \alpha < n$.
