Analysis and Probability seminar

Abstract: The Ornstein-Uhlenbeck operator is a partial differential operator in R^n. We modify it by letting the drift go outwards instead of inwards. As a basic, underlying measure one then takes, instead of a Gaussian measure, its inverse, which is a measure with a density like exp (|x|^2). It is now natural to form the corresponding semigroup and ask which properties of the Ornstein-Uhlenbeck semigroup carry over to this ”inverse” semigroup. We start answering this question by showing that the maximal operator of the semigroup is bounded on L^p, 1 < p < ∞, with respect to the inverse Gaussian measure, and of weak type 1,1.