The optimal hypercontractive constants for ${\mathbb{Z}}_3$ and biased Bernoulli random variables

Jie Cao, Shilei Fan, Yong Han +2

We resolve a folklore problem of determining the optimal hypercontractive constants $r_{p,q}({\mathbb{Z}}_3)$ for the cyclic group ${\mathbb{Z}}_3$ for all $1<p<q<\infty$. More p…