The maximal operator associated to a non-symmetric Ornstein-Uhlenbeck semigroup
Abstract
Description
Let (H_t) be the Ornstein-Uhlenbeck semigroup on R^d with covariance matrix I and drift matrix λ(R-I), where λ>0 and R is a skew-adjoint matrix and denote by γ_\infty the invariant measure for (H_t). Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L^2(γ_\infty). We prove that if the matrix R generates a one-parameter group of periodic rotations then the maximal operator associated to the semigroup is of weak type 1 with respect to the invariant measure. We also prove that the maximal operator associated to an arbitrary normal Ornstein-Uhlenbeck semigroup is bounded on L^p(γ_\infty) if and only if 1<p\le \infty.
20 pages, to appear in J Fourier Anal Appl, available on line at http://www.springerlink.com
20 pages, to appear in J Fourier Anal Appl, available on line at http://www.springerlink.com