{
  "id": "1910.07837",
  "version": "v1",
  "published": "2019-10-17T11:46:29.000Z",
  "updated": "2019-10-17T11:46:29.000Z",
  "title": "On Hausdorff measure and an inequality due to Maz'ya",
  "authors": [
    "Hendrik Vogt",
    "Jürgen Voigt"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We give an \"elementary\" proof of an inequality due to Maz'ya. As a prerequisite we prove an approximation property for the Hausdorff measure. We also comment on the relations between Maz'ya's inequality, the isoperimetric inequality and the Sobolev inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-17T11:46:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q15",
      "28A75",
      "46E35"
    ],
    "keywords": [
      "hausdorff measure",
      "isoperimetric inequality",
      "mazyas inequality",
      "sobolev inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}