Maximal Operators, Littlewood–Paley Functions and Variation Operators Associated with Nonsymmetric Ornstein–Uhlenbeck Operators

Abstract

In this paper, we establish L^p boundedness properties for maximal operators, Littlewood–Paley functions and variation operators involving Poisson semigroups and resolvent operators associated with nonsymmetric Ornstein–Uhlenbeck operators. We consider the Ornstein–Uhlenbeck operators defined by the identity as the covariance matrix and having a drift given by the matrix -lambda (I+R), being lambda >0 and R a skew-adjoint matrix. The semigroups associated with these Ornstein–Uhlenbeck operators are the basic building blocks of all the normal Ornstein–Uhlenbeck semigroups.