Advanced Studies in Pure Mathematics

Orlicz Norm Equivalence for the Ornstein-Uhlenbeck Operator

Ichiro Shigekawa

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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

Source
Stochastic Analysis and Related Topics in Kyoto: In honour of Kiyosi Itô, H. Kunita, S. Watanabe and Y. Takahashi, eds. (Tokyo: Mathematical Society of Japan, 2004), 301-317

Dates
Received: 20 March 2003
First available in Project Euclid: 3 January 2019

Permanent link to this document
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


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