Exponential inequalities in probability spaces revisited
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.
Authors
- Cyril Roberto (ORCID: https://orcid.org/0000-0003-0522-0101)
- Esther Bou Dagher (ORCID: https://orcid.org/0000-0003-3638-6593)
- Sergey G. Bobkov (ORCID: https://orcid.org/0000-0003-2838-5048)
- Ali Barki
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Minnesota (US)
- Université Paris Nanterre (FR)
- Mathématiques Appliquées à Paris 5 (FR)
- Imperial College London (GB)
- Université Paris Dauphine-PSL (FR)
Publication Details
- Journal
- Revista Matemática Iberoamericana
- Published
- 2026-06-19
- DOI
- https://doi.org/10.4171/rmi/1635
- Citations
- 1
- Primary Topic
- Advanced Banach Space Theory
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- Engineering and Physical Sciences Research Council