{
  "id": "1811.11118",
  "version": "v1",
  "published": "2018-11-27T17:30:43.000Z",
  "updated": "2018-11-27T17:30:43.000Z",
  "title": "Sobolev-Type Inequalities for Dunkl Operators",
  "authors": [
    "Andrei Velicu"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we study the Sobolev inequality in the Dunkl setting using two new approaches which provide a simpler elementary proof of the classical case $p=2$, as well as an extension to the coefficient $p=1$ that was previously unknown. We also find sharp constants for the Sobolev inequality in Weyl chambers and on the whole space $\\mathbb{R}^N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-27T17:30:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dunkl operators",
      "sobolev-type inequalities",
      "sobolev inequality",
      "simpler elementary proof",
      "sharp constants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}