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arXiv · 2407.15262

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

Pablo Rocha
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Abstract

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 $0 < \alpha < n$.

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Pablo Rocha. 2024-07-21. A note about the discrete Riesz potential on $\mathbb{Z}^n$. https://arxiv.org/abs/2407.15262

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