The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910036258717696 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | In [J. Class. Anal., vol. 26 (1) (2025), 63-76], we proved that the discrete Riesz potential $I_α$ is a bounded operator $H^p(\mathbb{Z}^n) \to H^q(\mathbb{Z}^n)$ for $\frac{n-1}{n} < p \leq 1$, $\frac{1}{q} = \frac{1}{p} - \fracα{n}$ and $0 < α< n$. In this note, we extend such boundedness on the full range $0 < p \leq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential Rocha, Pablo Classical Analysis and ODEs In [J. Class. Anal., vol. 26 (1) (2025), 63-76], we proved that the discrete Riesz potential $I_α$ is a bounded operator $H^p(\mathbb{Z}^n) \to H^q(\mathbb{Z}^n)$ for $\frac{n-1}{n} < p \leq 1$, $\frac{1}{q} = \frac{1}{p} - \fracα{n}$ and $0 < α< n$. In this note, we extend such boundedness on the full range $0 < p \leq 1$. |
| title | The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.20342 |