If Q is a real, symmetric and positive definite n×n matrix, and B
a real n×n matrix whose eigenvalues have negative real parts, we
consider the Ornstein--Uhlenbeck semigroup on Rn with covariance
Q and drift matrix B. Our main result says that the associated maximal
operator is of weak type (1,1) with respect to the invariant measure. The
proof has a geometric gist and hinges on the "forbidden zones method"
previously introduced by the third author.Comment: 21 pages. Introduction revised. Some changes in Sections 3 and