Classical discrete operators on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914959556870144 |
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| author | Rocha, Pablo |
| author_facet | Rocha, Pablo |
| contents | We show, by applying discrete weighted norm inequalities and the Rubio de Francia algorithm, that the discrete Hilbert transform and discrete Riesz potential are bounded on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces whenever the discrete Hardy-Littlewood maximal is bounded on $\ell^{p'(\cdot)}(\mathbb{Z})$. We also obtain vector-valued inequalities for the discrete fractional maximal operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical discrete operators on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces Rocha, Pablo Classical Analysis and ODEs Functional Analysis We show, by applying discrete weighted norm inequalities and the Rubio de Francia algorithm, that the discrete Hilbert transform and discrete Riesz potential are bounded on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces whenever the discrete Hardy-Littlewood maximal is bounded on $\ell^{p'(\cdot)}(\mathbb{Z})$. We also obtain vector-valued inequalities for the discrete fractional maximal operator. |
| title | Classical discrete operators on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2407.15726 |