The Ornstein-Uhlenbeck operator in Rn is  linear and  elliptic with constant second-order coefficients. But the first-order coefficients are linear in the coordinates and such that they cause a drift inwards. This operator generates a semigroup, and we study the corresponding maximal operator. The relevant measure here is a gaussian measure, which replaces
Lebesgue measure. 
  Assuming only that the semigroup is normal, i.e., commutes with
its adjoint, we prove that the maximal operator is of weak type (1,1) for the gaussian measure. This extends earlier results by several authors. The first step in the proof is a transformation of variables which gives the semigroup  a reasonable, explicit expression.

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