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

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(e^−t I) (−1 ≤ q ≤ 1), where Γ _q is a q-Gaussian functor.

Keywords

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

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