{
  "id": "1810.08845",
  "version": "v1",
  "published": "2018-10-20T19:34:54.000Z",
  "updated": "2018-10-20T19:34:54.000Z",
  "title": "Hardy, Hardy-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups",
  "authors": [
    "Michael Ruzhansky",
    "Nurgissa Yessirkegenov"
  ],
  "comment": "30 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we obtain two-weight Hardy inequalities on general metric measure spaces possessing polar decompositions. Moreover, we also find necessary and sufficient conditions for the weights for such inequalities to be true. As a consequence, we establish the Hardy, Hardy-Sobolev, Caffarelli-Kohn-Nirenberg, Gagliardo-Nirenberg inequalities and their critical versions on general connected Lie groups, which include both unimodular and non-unimodular cases in compact and noncompact settings. As a byproduct, it also gives, as a special case, an alternative proof for Sobolev embedding theorems on general (non-unimodular) Lie groups. We also obtain the corresponding uncertainty type principles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-20T19:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "22E30",
      "43A15"
    ],
    "keywords": [
      "general lie groups",
      "caffarelli-kohn-nirenberg inequalities",
      "spaces possessing polar decompositions",
      "hardy-sobolev",
      "metric measure spaces possessing polar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}