{
  "id": "1007.4086",
  "version": "v1",
  "published": "2010-07-23T09:45:39.000Z",
  "updated": "2010-07-23T09:45:39.000Z",
  "title": "Improved Sobolev Inequalities and Muckenhoupt weights on stratified Lie groups",
  "authors": [
    "Diego Chamorro"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study in this article the Improved Sobolev inequalities with Muckenhoupt weights within the framework of stratified Lie groups. This family of inequalities estimate the Lq norm of a function by the geometric mean of two norms corresponding to Sobolev spaces W(s;p) and Besov spaces B(-b, infty, infty). When the value p which characterizes Sobolev space is strictly larger than 1, the required result is well known in R^n and is classically obtained by a Littlewood-Paley dyadic blocks manipulation. For these inequalities we will develop here another totally different technique. When p = 1, these two techniques are not available anymore and following M. Ledoux in R^n, we will treat here the critical case p = 1 for general stratified Lie groups in a weighted functional space setting. Finally, we will go a step further with a new generalization of Improved Sobolev inequalities using weak-type Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-23T09:45:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sobolev inequalities",
      "muckenhoupt weights",
      "littlewood-paley dyadic blocks manipulation",
      "general stratified lie groups",
      "weak-type sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4086C"
    }
  }
}