Logarithmic sobolev inequalities and exponential integrability

Shigeki Aida; Takao Masuda; Ichiro Shigekawa

doi:10.1006/jfan.1994.1142

Logarithmic sobolev inequalities and exponential integrability

Shigeki Aida, Takao Masuda, Ichiro Shigekawa

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

80 Citations (Scopus)

Abstract

We prove the exponential integrability of Lipschitz functions in abstract Wiener spaces by using logarithmic Sobolev inequalities. We introduce two notions of Lipschitz continuity and apply the method of Davis and Simon [J. Funct. Anal.59 (1984), 335-395] to prove our main theorem. Moreover we give several conditions under which the function is exponentially integrable.

Original language	English
Pages (from-to)	83-101
Number of pages	19
Journal	Journal of Functional Analysis
Volume	126
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1994.1142
Publication status	Published - 1994 Nov 15

ASJC Scopus subject areas

Analysis

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10.1006/jfan.1994.1142

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abstract = "We prove the exponential integrability of Lipschitz functions in abstract Wiener spaces by using logarithmic Sobolev inequalities. We introduce two notions of Lipschitz continuity and apply the method of Davis and Simon [J. Funct. Anal.59 (1984), 335-395] to prove our main theorem. Moreover we give several conditions under which the function is exponentially integrable.",

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AB - We prove the exponential integrability of Lipschitz functions in abstract Wiener spaces by using logarithmic Sobolev inequalities. We introduce two notions of Lipschitz continuity and apply the method of Davis and Simon [J. Funct. Anal.59 (1984), 335-395] to prove our main theorem. Moreover we give several conditions under which the function is exponentially integrable.

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Logarithmic sobolev inequalities and exponential integrability

Abstract

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