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arXiv · 2607.19769

The missing two-point inequality in Weissler's conjecture

Yi C. Huang·Paata Ivanisvili
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Abstract

Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges $2<p\le q<3$ and $\frac32<p\le q<2$. Ivanisvili--Nazarov established the diagonal cases. We prove the remaining strict off-diagonal cases through the corresponding two-point inequality. In fact, our argument proves the two-point inequality for every $2<p<q<\infty$ and, by duality, for every $1<p<q<2$.

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Yi C. Huang, Paata Ivanisvili. 2026-07-22. The missing two-point inequality in Weissler's conjecture. https://arxiv.org/abs/2607.19769

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