A molecular decomposition for $H^p(\mathbb{Z}^n)$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914953241296896 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | In this work, for the range $\frac{n-1}{n} < p \leq 1$, we give a molecular reconstruction theorem for $H^p(\mathbb{Z}^n)$. As an application of this result and the atomic decomposition developed by S. Boza and M. Carro in [Proc. R. Soc. Edinb., 132 A (1) (2002), 25-43], we prove that the discrete Riesz potential $I_α$ defined on $\mathbb{Z}^n$ is a bounded operator $H^p(\mathbb{Z}^n) \to H^q(\mathbb{Z}^n)$ for $\frac{n-1}{n} < p < \frac{n}α$ and $\frac{1}{q} = \frac{1}{p} - \fracα{n}$, where $0 < α< n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A molecular decomposition for $H^p(\mathbb{Z}^n)$ Rocha, Pablo Classical Analysis and ODEs In this work, for the range $\frac{n-1}{n} < p \leq 1$, we give a molecular reconstruction theorem for $H^p(\mathbb{Z}^n)$. As an application of this result and the atomic decomposition developed by S. Boza and M. Carro in [Proc. R. Soc. Edinb., 132 A (1) (2002), 25-43], we prove that the discrete Riesz potential $I_α$ defined on $\mathbb{Z}^n$ is a bounded operator $H^p(\mathbb{Z}^n) \to H^q(\mathbb{Z}^n)$ for $\frac{n-1}{n} < p < \frac{n}α$ and $\frac{1}{q} = \frac{1}{p} - \fracα{n}$, where $0 < α< n$. |
| title | A molecular decomposition for $H^p(\mathbb{Z}^n)$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2408.09528 |