The Equivalence of Hypercontractivity and Logarithmic Sobolev Inequality for q (−1 ≤ q ≤ 1) -Ornstein-Uhlenbeck Semigroup

The Equivalence of Hypercontractivity and Logarithmic Sobolev Inequality for q (−1 ≤ q ≤ 1) -Ornstein-Uhlenbeck Semigroup

In this paper the author proves the equivalence of hypercontractivity and logarithmic Sobolev inequality for q -Ornstein-Uhlenbeck semigroup U t ( q ) = Γ q (e − t I ) (−1 ≤ q ≤ 1), where Γ q is a q -Gaussian functor.

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Veröffentlicht in:Chinese annals of mathematics. Serie B 2020-07, Vol.41 (4), p.615-626
1. Verfasser: Zhang, Lunchuan
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Equivalence
Mathematics
Mathematics and Statistics
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Zusammenfassung:In this paper the author proves the equivalence of hypercontractivity and logarithmic Sobolev inequality for q -Ornstein-Uhlenbeck semigroup U t ( q ) = Γ q (e − t I ) (−1 ≤ q ≤ 1), where Γ q is a q -Gaussian functor.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-020-0221-x