{
  "id": "2306.00209",
  "version": "v1",
  "published": "2023-05-31T21:58:34.000Z",
  "updated": "2023-05-31T21:58:34.000Z",
  "title": "Exponential inequalities in probability spaces revisited",
  "authors": [
    "Ali Barki",
    "Sergey G. Bobkov",
    "Esther Bou Dagher",
    "Cyril Roberto"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-31T21:58:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability spaces",
      "exponential inequalities",
      "moser-trudinger-type inequalities",
      "exponential integrability",
      "ivanisvili-russells inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}