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arXiv · 2507.06115

Optimal Young's convolutions inequality and its reverse form on the hypercube

David Beltran·Paata Ivanisvili·José Madrid·Lekha Patil
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Abstract

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 $r = 2$.

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David Beltran, Paata Ivanisvili, José Madrid, Lekha Patil. 2025-07-08. Optimal Young's convolutions inequality and its reverse form on the hypercube. https://arxiv.org/abs/2507.06115

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