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VOL. 41 | 2004 Orlicz Norm Equivalence for the Ornstein-Uhlenbeck Operator
Ichiro Shigekawa

Editor(s) Hiroshi Kunita, Shinzo Watanabe, Yoichiro Takahashi

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.

Information

Published: 1 January 2004
First available in Project Euclid: 3 January 2019

zbMATH: 1063.60083
MathSciNet: MR2083716

Digital Object Identifier: 10.2969/aspm/04110301

Rights: Copyright © 2004 Mathematical Society of Japan

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