  For $0<s<1$, we consider the Dirichlet problem for the fractional nonlocal
Ornstein--Uhlenbeck equation $$\begin{cases}
(-\Delta+x\cdot\nabla)^su=f&\hbox{in}~\Omega\\ u=0&\hbox{on}~\partial\Omega,
\end{cases}$$ where $\Omega$ is a possibly unbounded open subset of
$\mathbb{R}^n$, $n\geq2$. The appropriate functional settings for this nonlocal
equation and its corresponding extension problem are developed. We apply
Gaussian symmetrization techniques to derive a concentration comparison
estimate for solutions. As consequences, novel $L^p$ and $L^p(\log L)^\alpha$
regularity estimates in terms of the datum $f$ are obtained by comparing $u$
with half-space solutions.
