3 problems

Talagrand's convolution conjecture. For every $t>0$ there exists a function $\psi_t:[1,\infty) \to [1,\infty)$ such that $\psi_t(u) \to \infty$ as $u \to \infty$, and for every…

Let $n\geq 1$, let $\gamma_n$ be the standard Gaussian probability measure on $\mathbb{R}^n$, and let $P_s$ be the Ornstein–Uhlenbeck semigroup. For every non-negative measurable f…

Let $\gamma_n$ be the standard Gaussian measure on $\mathbb R^n$, and let $(Q_t)$ be the Ornstein–Uhlenbeck semigroup defined by … For a non-negative function $f$ of integral $1$,…