{
  "id": "1403.0215",
  "version": "v2",
  "published": "2014-03-02T14:49:09.000Z",
  "updated": "2015-03-06T09:58:48.000Z",
  "title": "Hardy Type Inequalities for $Δ_λ$-Laplacians",
  "authors": [
    "A. E. Kogoj",
    "S. Sonner"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\\Delta_\\lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained for Grushin type operators $$ \\Delta_{x}+ |x|^{2\\alpha}\\Delta_{y},\\qquad\\ (x,y)\\in\\mathbb{R}^{N_1}\\times\\mathbb{R}^{N_2},\\ \\alpha\\geq 0, $$ which were proved to be sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-02T14:49:09.000Z",
      "abstract": "We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\\Delta_\\lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained for Grushin type operators $$\\Delta_{x}+ |x|^{2\\alpha}\\Delta_{y},\\qquad\\ (x,y)\\in\\R^{N_1}\\times\\R^{N_2},\\ \\alpha\\geq 0,$$ which were proved to be sharp.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-06T09:58:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H20",
      "26D10",
      "35H10"
    ],
    "keywords": [
      "laplacians",
      "derive hardy type inequalities",
      "grushin type operators",
      "sub-elliptic operators",
      "explicit values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.0215K"
    }
  }
}