2026/07/22 by Yi C. Huang, Paata Ivanisvili
#math.FA #math.CA #math.CV
Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges 2<p≤ q<3 and \frac32<p≤ 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<∞ and, by duality, for every 1<p<q<2.