The missing two-point inequality in Weissler's conjecture

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 $1<p<q<2$.

Disclosure

“over the years. P. I. acknowledges partial support from the US NSF CAREER grant DMS-2152401, US NSF grant DMS-2554183, a Simons Fellowship, and a Humboldt Research Fellowship for Experienced Researchers. The authors acknowledge the use of AI tools. All mathematical arguments and proofs in the final manuscript were checked and written by the authors. References [1] Dominique Bakry, Ivan Gentil, and Michel Ledoux, Analysis and geometry of Ma”

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2026-08-23T19:01:46.203507Z

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