On $\mathbf R^d$ the Ornstein-Uhlenbeck operator is defined as ($\partial_i = \frac{\partial}{\partial x_i}$).

$$L = \frac12 \sum_i \partial_i^* \partial_i$$

where $\partial_i^* = -\partial_i + 2 x_i$.

Now we can form the semigroup $e^{-t L}$ and the corresponding maximal function

$$M^* f(x) = \sup_{t > 0} \left |e^{-t L} f(x) \right |, \quad f \in L^1(\gamma)$$

where $\gamma$ is the Gaussian measure $\gamma(x) = \pi^{-d/2} e^{-|x|^2} dx$.

Now the claim is that $M^*$ is of weak $(p, p)$ type for $1 < p < \infty$. How do I show this? Any references?