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