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| The Equivalence of Hypercontractivity and Logarithmic Sobolev Inequality for q ((1 ≤ q ≤ 1) -Ornstein-Uhlenbeck Semigroup |
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Citation： |
Lunchuan ZHANG.The Equivalence of Hypercontractivity and Logarithmic Sobolev Inequality for q ((1 ≤ q ≤ 1) -Ornstein-Uhlenbeck Semigroup[J].Chinese Annals of Mathematics B,2020,41(4):615~626 |
| Page view： 432
Net amount： 466 |
Authors： |
Lunchuan ZHANG; |
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| Abstract： |
In this paper the author proves the equivalence of hypercontractivity and logarithmic Sobolev inequality for q-Ornstein-Uhlenbeck semigroup Ut(q) = Γq(e-tI) ((1 ≤ q ≤ 1), where Γq is a q-Gaussian functor. |
Keywords： |
q-Ornstein-Uhlenbeck semigroup, Hypercontractivity, Logarithmic Sobolev inequality |
Classification： |
47D03, 58G32, 46L50, 46L70 |
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