{
  "id": "1809.09957",
  "version": "v1",
  "published": "2018-09-26T13:12:23.000Z",
  "updated": "2018-09-26T13:12:23.000Z",
  "title": "Isomorphisms between spaces of Lipschitz functions",
  "authors": [
    "Leandro Candido",
    "Marek Cúth",
    "Michal Doucha"
  ],
  "comment": "27 pages, no figures",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We develop tools for proving isomorphisms of normed spaces of Lipschitz functions over various doubling metric spaces and Banach spaces. In particular, we show that $\\operatorname{Lip}_0(\\mathbb{Z}^d)\\simeq\\operatorname{Lip}_0(\\mathbb{R}^d)$, for all $d\\in\\mathbb{N}$. More generally, we e.g. show that $\\operatorname{Lip}_0(\\Gamma)\\simeq \\operatorname{Lip}_0(G)$, where $\\Gamma$ is from a large class of finitely generated nilpotent groups and $G$ is its Mal'cev closure; or that $\\operatorname{Lip}_0(\\ell_p)\\simeq\\operatorname{Lip}_0(L_p)$, for all $1\\leq p<\\infty$. We leave a large area for further possible research.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-26T13:12:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lipschitz functions",
      "isomorphisms",
      "large area",
      "malcev closure",
      "doubling metric spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}