{
  "id": "1610.03379",
  "version": "v1",
  "published": "2016-10-11T14:58:49.000Z",
  "updated": "2016-10-11T14:58:49.000Z",
  "title": "Sobolev inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groups",
  "authors": [
    "Michael Ruzhansky",
    "Durvudkhan Suragan",
    "Nurgissa Yessirkegenov"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1603.06239",
  "categories": [
    "math.FA"
  ],
  "abstract": "We define Euler-Hilbert-Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are homogeneous differential operators of order zero. Sharp remainder terms of $L^{p}$ and weighted Sobolev and Sobolev-Rellich inequalities on homogeneous groups are given. Most inequalities are obtained with best constants. As consequences, we obtain analogues of the generalised classical Sobolev and Sobolev-Rellich inequalities. We also discuss applications of logarithmic Hardy inequalities to Sobolev-Lorentz-Zygmund spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T14:58:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E30",
      "46E35"
    ],
    "keywords": [
      "homogeneous groups",
      "sobolev-lorentz-zygmund spaces",
      "sobolev inequalities",
      "sobolev-rellich inequalities",
      "logarithmic hardy inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}