{
  "id": "2001.05932",
  "version": "v1",
  "published": "2020-01-16T16:49:34.000Z",
  "updated": "2020-01-16T16:49:34.000Z",
  "title": "Poincaré and Hardy inequalities on homogeneous trees",
  "authors": [
    "Elvise Berchio",
    "Federico Santagati",
    "Maria Vallarino"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We study Hardy-type inequalities on infinite homogeneous trees. More precisely, we derive optimal Hardy weights for the combinatorial Laplacian in this setting and we obtain, as a consequence, optimal improvements for the Poincar\\'e inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-16T16:49:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "39A12",
      "05C05"
    ],
    "keywords": [
      "hardy inequalities",
      "derive optimal hardy weights",
      "study hardy-type inequalities",
      "infinite homogeneous trees",
      "combinatorial laplacian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}