Dimension-free estimates for discrete maximal functions related to normalized gaussians
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917957138907136 |
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| author | Mirek, Mariusz Szarek, Tomasz Z. Wróbel, Błażej |
| author_facet | Mirek, Mariusz Szarek, Tomasz Z. Wróbel, Błażej |
| contents | In this paper, we investigate dimension-free estimates for maximal operators of convolutions with discrete normalized Gaussians (related to the Theta function) in the context of maximal, jump and $r$-variational inequalities on $\ell^p(\mathbb{Z}^d)$ spaces. This is the first instance of a discrete operator in the literature where $\ell^p(\mathbb{Z}^d)$ bounds are provided for the entire range of $1 < p < \infty$. The methods of proof rely on developing robust Fourier methods, which are combined with the fractional derivative, a tool that has not been previously applied to studying similar questions in the discrete setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension-free estimates for discrete maximal functions related to normalized gaussians Mirek, Mariusz Szarek, Tomasz Z. Wróbel, Błażej Classical Analysis and ODEs Functional Analysis 42B25, 42B15 In this paper, we investigate dimension-free estimates for maximal operators of convolutions with discrete normalized Gaussians (related to the Theta function) in the context of maximal, jump and $r$-variational inequalities on $\ell^p(\mathbb{Z}^d)$ spaces. This is the first instance of a discrete operator in the literature where $\ell^p(\mathbb{Z}^d)$ bounds are provided for the entire range of $1 < p < \infty$. The methods of proof rely on developing robust Fourier methods, which are combined with the fractional derivative, a tool that has not been previously applied to studying similar questions in the discrete setting. |
| title | Dimension-free estimates for discrete maximal functions related to normalized gaussians |
| topic | Classical Analysis and ODEs Functional Analysis 42B25, 42B15 |
| url | https://arxiv.org/abs/2503.11259 |