{
  "id": "1610.07032",
  "version": "v1",
  "published": "2016-10-22T11:04:39.000Z",
  "updated": "2016-10-22T11:04:39.000Z",
  "title": "Anisotropic $L^{2}$-weighted Hardy and $L^{2}$-Caffarelli-Kohn-Nirenberg inequalities",
  "authors": [
    "Michael Ruzhansky",
    "Durvudkhan Suragan"
  ],
  "comment": "Commun. Contemp. Math. (to appear)",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "We establish sharp remainder terms of the $L^{2}$-Caffarelli-Kohn-Niren\\-berg inequalities on homogeneous groups, yielding the inequalities with best constants. Our methods also give new sharp Caffarelli-Kohn-Nirenberg type inequalities in $\\mathbb{R}^{n}$ with arbitrary quasi-norms. We also present explicit examples to illustrate our results for different weights and in abelian cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-22T11:04:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "caffarelli-kohn-nirenberg inequalities",
      "weighted hardy",
      "anisotropic",
      "sharp caffarelli-kohn-nirenberg type inequalities",
      "establish sharp remainder terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}