A note about the discrete Riesz potential on $\mathbb{Z}^n$

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 $0＜p\leq1$ and $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{n}$, where $0＜\alpha＜n$.