{
  "id": "2204.06636",
  "version": "v1",
  "published": "2022-04-13T20:55:52.000Z",
  "updated": "2022-04-13T20:55:52.000Z",
  "title": "Characterizations of fractional Sobolev--Poincaré and (localized) Hardy inequalities",
  "authors": [
    "Firoj Sk"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper, we prove capacitary versions of the fractional Sobolev--Poincar\\'e inequalities. We characterize localized variant of the boundary fractional Sobolev--Poincar\\'e inequalities through uniform fatness condition of the domain in $\\mathbb{R}^n$. Existence type results on the fractional Hardy inequality are established in the supercritical case $sp>n$ for $s\\in(0,1)$, $p>1$. Characterization of the fractional Hardy inequality through weak supersolution of the associate problem is also addressed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-13T20:55:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B15",
      "35A23",
      "46E35",
      "49R05"
    ],
    "keywords": [
      "fractional hardy inequality",
      "characterization",
      "boundary fractional sobolev-poincare inequalities",
      "uniform fatness condition",
      "existence type results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}