The missing two-point inequality in Weissler's conjecture

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 $1<p<q<2$.