Orlicz Norm Equivalence for the Ornstein-Uhlenbeck Operator

Abstract

The Meyer equivalence on an abstract Wiener space states that the $L^p$-norm of square root of the Ornstein-Uhlenbeck operator is equivalent to $L^p$-norm of the Malliavin derivative. We prove the equivalence in the framework of Orlicz space. We also discuss the logarithmic Sobolev inequality in $L^p$ setting and higher order logarithmic Sobolev inequality.