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

2025/07/08 by Beltran, David, Ivanisvili, Paata, Madrid, José +1
#11B13 #11B30 #26D15 #39A12 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.06115

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≠ q, providing necessary conditions for the inequality to hold, along with partial results in the case r = 2.

Citations

• Inequalities in Fourier analysis on binary cubes
• Sharp estimates for Gowers norms on discrete cubes
• Discrete Brunn-Minkowski Inequality for subsets of the cube
• Additive energies on discrete cubes
• A bound on partitioning clusters
• Energies and structure of additive sets
• Higher moments of convolutions

Cited by

• Functional Inequalities and Random Walks on Increasing Subsets of the Hypercube

Related

• Optimal Young's inequality and its converse:a simple proof
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• On suprema of convolutions on discrete cubes
• Inequalities in Fourier analysis on binary cubes
• Near-extremizers of Young's Inequality for R^d