Remark on dimension-free estimates for discrete maximal functions over $\ell^q$ balls: small dyadic scales
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912499974012928 |
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| author | Niksiński, Jakub |
| author_facet | Niksiński, Jakub |
| contents | We give a dimension-free bound on $\ell^p(\mathbb{Z} ^d)$, $p \in [2, \infty]$ for the discrete Hardy-Littlewood maximal operator over the $\ell^q$ balls in $\mathbb{Z} ^d$ with small dyadic radii. Our result combined with the work of Kosz, Mirek, Plewa, Wróbel gives dimension-free estimates on $\ell^p(\mathbb{Z}^d)$, $p \in [2, \infty]$ for the discrete dyadic Hardy-Littlewood maximal operator over $\ell^q$ balls for $q \geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remark on dimension-free estimates for discrete maximal functions over $\ell^q$ balls: small dyadic scales Niksiński, Jakub Classical Analysis and ODEs 42B15, 42B25 We give a dimension-free bound on $\ell^p(\mathbb{Z} ^d)$, $p \in [2, \infty]$ for the discrete Hardy-Littlewood maximal operator over the $\ell^q$ balls in $\mathbb{Z} ^d$ with small dyadic radii. Our result combined with the work of Kosz, Mirek, Plewa, Wróbel gives dimension-free estimates on $\ell^p(\mathbb{Z}^d)$, $p \in [2, \infty]$ for the discrete dyadic Hardy-Littlewood maximal operator over $\ell^q$ balls for $q \geq 2$. |
| title | Remark on dimension-free estimates for discrete maximal functions over $\ell^q$ balls: small dyadic scales |
| topic | Classical Analysis and ODEs 42B15, 42B25 |
| url | https://arxiv.org/abs/2410.23993 |