A unification of the hypercontractivity and its exponential variant of the Ornstein-Uhlenbeck semigroup

Yuu Hariya

Let ${\gamma }_d$ be the $d$-dimensional standard Gaussian measure and $\{Q_t{\}}_{t\ge 0}$ the Ornstein-Uhlenbeck semigroup acting on $L^1({\gamma }_d)$. We show that the hypercontractivity…