## Advanced Studies in Pure Mathematics

### Orlicz Norm Equivalence for the Ornstein-Uhlenbeck Operator

Ichiro Shigekawa

#### 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.

#### Article information

Dates
First available in Project Euclid: 3 January 2019

https://projecteuclid.org/ euclid.aspm/1546542618

Digital Object Identifier
doi:10.2969/aspm/04110301

Mathematical Reviews number (MathSciNet)
MR2083716

Zentralblatt MATH identifier
1063.60083

#### Citation

Shigekawa, Ichiro. Orlicz Norm Equivalence for the Ornstein-Uhlenbeck Operator. Stochastic Analysis and Related Topics in Kyoto: In honour of Kiyosi Itô, 301--317, Mathematical Society of Japan, Tokyo, Japan, 2004. doi:10.2969/aspm/04110301. https://projecteuclid.org/euclid.aspm/1546542618