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

Lunchuan Zhang

Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (4) : 615 -626.

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Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (4) : 615 -626. DOI: 10.1007/s11401-020-0221-x
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The Equivalence of Hypercontractivity and Logarithmic Sobolev Inequality for q (−1 ≤ q ≤ 1) -Ornstein-Uhlenbeck Semigroup

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Abstract

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

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q-Ornstein-Uhlenbeck semigroup / Hypercontractivity / Logarithmic Sobolev inequality

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Lunchuan Zhang. The Equivalence of Hypercontractivity and Logarithmic Sobolev Inequality for q (−1 ≤ q ≤ 1) -Ornstein-Uhlenbeck Semigroup. Chinese Annals of Mathematics, Series B, 2020, 41(4): 615-626 DOI:10.1007/s11401-020-0221-x

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