Fractional series operators on $\mathbb{Z}^n$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912551954022400 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | For $0 \leq α< n$ and $m \in \mathbb{N} \cap (1 - \fracα{n}, \, \infty)$, we introduce a class of fractional series operators $T_{α, m}$ defined on $\mathbb{Z}^n$ which are generated by certain $m$-invertible matrices with integer coefficients. In this note, we prove that $T_{α, m}$ is a bounded operator $H^p(\mathbb{Z}^n) \to \ell^q(\mathbb{Z}^n)$ for $0 < p < \frac{n}α$ and $\frac{1}{q} = \frac{1}{p} - \fracα{n}$. This generalizes the results obtained by the author in [Acta Math. Hungar., 168 (1) (2022), 202-216]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_17470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional series operators on $\mathbb{Z}^n$ Rocha, Pablo Classical Analysis and ODEs For $0 \leq α< n$ and $m \in \mathbb{N} \cap (1 - \fracα{n}, \, \infty)$, we introduce a class of fractional series operators $T_{α, m}$ defined on $\mathbb{Z}^n$ which are generated by certain $m$-invertible matrices with integer coefficients. In this note, we prove that $T_{α, m}$ is a bounded operator $H^p(\mathbb{Z}^n) \to \ell^q(\mathbb{Z}^n)$ for $0 < p < \frac{n}α$ and $\frac{1}{q} = \frac{1}{p} - \fracα{n}$. This generalizes the results obtained by the author in [Acta Math. Hungar., 168 (1) (2022), 202-216]. |
| title | Fractional series operators on $\mathbb{Z}^n$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.17470 |