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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.06115 |
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| _version_ | 1866911045582323712 |
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| author | Beltran, David Ivanisvili, Paata Madrid, José Patil, Lekha |
| author_facet | Beltran, David Ivanisvili, Paata Madrid, José Patil, Lekha |
| contents | We establish sharp forms of Young's convolution inequality and its reverse on the discrete hypercube $\{0,1\}^d$ in the diagonal case $p=q$. As applications, we derive bounds for additive energies and sumsets. We also investigate the non-diagonal regime $p\neq q$, providing necessary conditions for the inequality to hold, along with partial results in the case $r = 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Young's convolutions inequality and its reverse form on the hypercube Beltran, David Ivanisvili, Paata Madrid, José Patil, Lekha Classical Analysis and ODEs Combinatorics 39A12, 26D15, 11B30, 11B13 We establish sharp forms of Young's convolution inequality and its reverse on the discrete hypercube $\{0,1\}^d$ in the diagonal case $p=q$. As applications, we derive bounds for additive energies and sumsets. We also investigate the non-diagonal regime $p\neq q$, providing necessary conditions for the inequality to hold, along with partial results in the case $r = 2$. |
| title | Optimal Young's convolutions inequality and its reverse form on the hypercube |
| topic | Classical Analysis and ODEs Combinatorics 39A12, 26D15, 11B30, 11B13 |
| url | https://arxiv.org/abs/2507.06115 |