Exponential inequalities in probability spaces revisited
Probability
2023-12-19 v2 Functional Analysis
Abstract
We revisit several results on exponential integrability in probability spaces and derive some new ones. In particular, we give a quantitative form of recent results by Cianchi-Musil and Pick in the framework of Moser-Trudinger-type inequalities, and recover Ivanisvili-Russell's inequality for the Gaussian measure. One key ingredient is the use of a dual argument, which is new in this context, that we also implement in the discrete setting of the Poisson measure on integers.
Keywords
Cite
@article{arxiv.2306.00209,
title = {Exponential inequalities in probability spaces revisited},
author = {Ali Barki and Sergey G. Bobkov and Esther Bou Dagher and Cyril Roberto},
journal= {arXiv preprint arXiv:2306.00209},
year = {2023}
}