The maximal operator of a normal Ornstein--Uhlenbeck semigroup is of weak type (1,1).
Consider a normal Ornstein--Uhlenbeck semigroup in Rn,
whose covariance is given by a positive definite matrix.
The drift matrix is assumed to have eigenvalues only in the left half-plane.
We prove that the associated maximal operator
is of weak type (1,1) with respect to the invariant measure.
This extends earlier work by G. Mauceri and L. Noselli.
The proof goes via the special case where the
matrix defining the covariance is
and the drift matrix is diagonal.