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 . 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 , the resulting operator is shown to be of strong type.