Maximal operators related to the Ornstein–Uhlenbeck semigroup with complex time parameter

Let γ be the Gaussian measure in Rd and Ht , t > 0, the corresponding Ornstein–Uhlenbeck semigroup, whose infinitesimal generator is −12 +x · grad. For each p with 12 this operator is of weak type but not of strong type (p,p) for γ . However, if a neighbourhood of the origin is deleted from Ep in the definition of H∗p, the resulting operator is shown to be of strong type. © 2005 Elsevier Inc. All rights reserved.