Soit la mesure Gaussienne standard sur et soit le semi-groupe d’Ornstein-Uhlenbeck. Eldan et Lee ont montré récemment que pour toute fonction positive d’intégrale et pour temps la queue de distribution de vérifie
où est une constante dépendant seulement de et pas de la dimension. L’objet de cet article est de simplifier en partie leur démonstration et d’éliminer le facteur .
Let be the standard Gaussian measure on and let be the Ornstein-Uhlenbeck semigroup. Eldan and Lee recently established that for every non-negative function of integral and any time the following tail inequality holds true:
where is a constant depending on but not on the dimension. The purpose of the present paper is to simplify parts of their argument and to remove the factor.
@article{AFST_2016_6_25_1_191_0, author = {Lehec, Joseph}, title = {Regularization in $L_1$ for the {Ornstein-Uhlenbeck} semigroup}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {191--204}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 25}, number = {1}, year = {2016}, doi = {10.5802/afst.1492}, zbl = {1336.60032}, mrnumber = {3485296}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1492/} }
TY - JOUR AU - Lehec, Joseph TI - Regularization in $L_1$ for the Ornstein-Uhlenbeck semigroup JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2016 DA - 2016/// SP - 191 EP - 204 VL - Ser. 6, 25 IS - 1 PB - Université Paul Sabatier, Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1492/ UR - https://zbmath.org/?q=an%3A1336.60032 UR - https://www.ams.org/mathscinet-getitem?mr=3485296 UR - https://doi.org/10.5802/afst.1492 DO - 10.5802/afst.1492 LA - en ID - AFST_2016_6_25_1_191_0 ER -
Lehec, Joseph. Regularization in $L_1$ for the Ornstein-Uhlenbeck semigroup. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 1, pp. 191-204. doi : 10.5802/afst.1492. http://archive.numdam.org/articles/10.5802/afst.1492/
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