A note about the discrete Riesz potential on $\mathbb{Z}^n$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910030504132608 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | In this note we prove that the discrete Riesz potential $I_α$ 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 $\frac{1}{q} = \frac{1}{p} - \fracα{n}$, where $0 < α< n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15262 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note about the discrete Riesz potential on $\mathbb{Z}^n$ Rocha, Pablo Classical Analysis and ODEs In this note we prove that the discrete Riesz potential $I_α$ 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 $\frac{1}{q} = \frac{1}{p} - \fracα{n}$, where $0 < α< n$. |
| title | A note about the discrete Riesz potential on $\mathbb{Z}^n$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2407.15262 |