{
  "id": "2101.06209",
  "version": "v1",
  "published": "2021-01-15T16:54:34.000Z",
  "updated": "2021-01-15T16:54:34.000Z",
  "title": "Hypercontractivity of the semigroup of the fractional laplacian on the n-sphere",
  "authors": [
    "Rupert L. Frank",
    "Paata Ivanisvili"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "For $1<p\\leq q$ we show that the Poisson semigroup $e^{-t\\sqrt{-\\Delta}}$ on the $n$-sphere is hypercontractive from $L^{p}$ to $L^{q}$ in dimensions $n \\leq 3$ if and only if $e^{-t\\sqrt{n}} \\leq \\sqrt{\\frac{p-1}{q-1}}$. We also show that the equivalence fails in large dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-15T16:54:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B62",
      "42B35",
      "47A30"
    ],
    "keywords": [
      "fractional laplacian",
      "hypercontractivity",
      "equivalence fails"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}