{
  "id": "1311.0094",
  "version": "v1",
  "published": "2013-11-01T06:06:20.000Z",
  "updated": "2013-11-01T06:06:20.000Z",
  "title": "Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group",
  "authors": [
    "Xiaolong Han"
  ],
  "comment": "To be published in Indiana University Mathematics Journal",
  "categories": [
    "math.CA",
    "math.OC"
  ],
  "abstract": "In this paper, we investigate the sharp Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. On one hand, we apply the concentration compactness principle to prove the existence of the maximizers. While the approach here gives a different proof under the special cases discussed in a recent work of Frank and Lieb, we generalize the result to all admissible cases. On the other hand, we provide the upper bounds of sharp constants for these inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-01T06:06:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B62",
      "49J45",
      "35R03"
    ],
    "keywords": [
      "heisenberg group",
      "maximizers",
      "sharp hardy-littlewood-sobolev inequalities",
      "concentration compactness principle",
      "upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0094H"
    }
  }
}