{
  "id": "0810.5259",
  "version": "v1",
  "published": "2008-10-29T12:13:30.000Z",
  "updated": "2008-10-29T12:13:30.000Z",
  "title": "Degenerate p-Laplacian operators on H-type groups and applications to Hardy type inequalities",
  "authors": [
    "Yongyang Jin",
    "Genkai Zhang"
  ],
  "comment": "Canadian Math. J., to appear",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Let $\\mathbb G$ be a step-two nilpotent group of H-type with Lie algebra $\\mathfrak G=V\\oplus \\mathfrak t$. We define a class of vector fields $X=\\{X_j\\}$ on $\\mathbb G$ depending on a real parameter $k\\ge 1$, and we consider the corresponding $p$-Laplacian operator $L_{p,k} u= \\text{div}_X (|\\na_{X} u|^{p-2} \\na_X u)$. For $k=1$ the vector fields $X=\\{X_j\\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$, for $k=2$ and $\\mathbb G$ being the Heisenberg group they are introduced by Greiner \\cite{Greiner-cjm79}. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-29T12:13:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hardy type inequality",
      "degenerate p-laplacian operators",
      "h-type groups",
      "invariant vector fields corresponding",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.5259J"
    }
  }
}