  We investigate $L^p(\gamma)$-$L^q(\gamma)$ off-diagonal estimates for the
Ornstein-Uhlenbeck semigroup $(e^{tL})_{t > 0}$. For sufficiently large $t$
(quantified in terms of $p$ and $q$) these estimates hold in an unrestricted
sense, while for sufficiently small $t$ they fail when restricted to maximal
admissible balls and sufficiently small annuli. Our counterexample uses Mehler
kernel estimates.

Functional Analysis;Classical Analysis and ODEs