Exponential inequalities in probability spaces revisited

Ali Barki, Sergey G. Bobkov, Esther Bou Dagher, Cyril Roberto

Published 2023-05-31Version 1

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.