On suprema of convolutions on discrete cubes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909972305018880 |
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| author | Gaitan, José Madrid, José |
| author_facet | Gaitan, José Madrid, José |
| contents | We find the optimal constant $C$ such that \begin{equation*} \|f_1*f_2*\dots*f_{k}\|_{\infty}\geq C\prod_{i=1}^{k}\|f_i\|_1 \end{equation*} for functions $f_i:\{0,1\}^d\to\mathbb{R}$. As applications, we derive bounds for Sidon sets on hypercubes, and, we also obtain bounds for the continuous analogue problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On suprema of convolutions on discrete cubes Gaitan, José Madrid, José Classical Analysis and ODEs Combinatorics 39A12, 26D15, 11B30, 11B13 We find the optimal constant $C$ such that \begin{equation*} \|f_1*f_2*\dots*f_{k}\|_{\infty}\geq C\prod_{i=1}^{k}\|f_i\|_1 \end{equation*} for functions $f_i:\{0,1\}^d\to\mathbb{R}$. As applications, we derive bounds for Sidon sets on hypercubes, and, we also obtain bounds for the continuous analogue problem. |
| title | On suprema of convolutions on discrete cubes |
| topic | Classical Analysis and ODEs Combinatorics 39A12, 26D15, 11B30, 11B13 |
| url | https://arxiv.org/abs/2512.18188 |