{
  "id": "1105.3082",
  "version": "v1",
  "published": "2011-05-16T12:47:19.000Z",
  "updated": "2011-05-16T12:47:19.000Z",
  "title": "Functional Inequalities and Subordination: Stability of Nash and Poincaré inequalities",
  "authors": [
    "René L. Schilling",
    "Jian Wang"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that certain functional inequalities, e.g.\\ Nash-type and Poincar\\'e-type inequalities, for infinitesimal generators of $C_0$ semigroups are preserved under subordination in the sense of Bochner. Our result improves \\cite[Theorem 1.3]{BM} by A.\\ Bendikov and P.\\ Maheux for fractional powers, and it also holds for non-symmetric settings. As an application, we will derive hypercontractivity, supercontractivity and ultracontractivity of subordinate semigroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-16T12:47:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional inequalities",
      "subordination",
      "non-symmetric settings",
      "fractional powers",
      "poincare-type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.3082S"
    }
  }
}