The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space are detected. The existence of extremal functions in the relevant inequalities is also established. Our results disclose analogies and dissimilarities in comparison with Adams' inequality for the Laplace operator, a companion of our inequalities in the Euclidean space.
Sharp exponential inequalities for the Ornstein-Uhlenbeck operator / Cianchi A.; Musil V.; Pick L.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 281:(2021), pp. 109217-109217. [10.1016/j.jfa.2021.109217]
Sharp exponential inequalities for the Ornstein-Uhlenbeck operator
Cianchi A.
;
2021
Abstract
The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space are detected. The existence of extremal functions in the relevant inequalities is also established. Our results disclose analogies and dissimilarities in comparison with Adams' inequality for the Laplace operator, a companion of our inequalities in the Euclidean space.
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