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Jun 23, 2020 at 17:11 comment added user69642 It is well hidden. Lemma 2.3 of this paper: sciencedirect.com/science/article/pii/S0022123602939789. Regarding the analyticity, it follows from Bismut formula together with this inequality.
Jun 23, 2020 at 17:01 comment added Paata Ivanishvili Do you happen to have a reference with applications to analyticity of the OU semigroup?
Jun 23, 2020 at 16:11 comment added user69642 Another inequality which has not been mentioned but which is very useful is the Carbery-Wright inequality which gives anti-concentration bound for polynomials of Gaussian random variables.
S Jun 23, 2020 at 8:10 history answered user69642 CC BY-SA 4.0
S Jun 23, 2020 at 8:10 history made wiki Post Made Community Wiki by user69642