{
  "id": "1405.2782",
  "version": "v2",
  "published": "2014-05-12T14:37:11.000Z",
  "updated": "2017-10-29T08:40:12.000Z",
  "title": "A Further Remark on Sobolev Spaces. The Case $0<p<1$",
  "authors": [
    "Aron Wennman"
  ],
  "comment": "5 pages, corrected typos",
  "categories": [
    "math.CA"
  ],
  "abstract": "We discuss a phenomenon observed by Jaak Peetre in the seventies: for small $L^{p}$-exponents, i.e. for $0<p<1$, the Sobolev spaces $W^{k,p}$ defined in a seemingly natural way are isomorphic to $L^{p}$. This says that the dual of $W^{k,p}$ is trivial, and indicates that these spaces are highly pathological. In this note we expand on Peetre's observation, explaining in detail some points that might merit further discussion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-12T14:37:11.000Z",
      "abstract": "We discuss a phenomenon observed by Jaak Peetre in the seventies: for small $L^{p}$-exponents, i.e. for $0<p<1$, the Sobolev spaces $W^{k,p}$ defined in a seemingly natural way are isomorphic to $L^{p}$. This says that the dual of $W^{k,p}$ is trivial, and indicates that these spaces are highly pathological. This is an interesting feature, but it seems like Peetre's proof is incomplete. The purpose of the present paper is to remedy this.",
      "comment": "5 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-10-29T08:40:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "sobolev spaces",
      "jaak peetre",
      "seemingly natural way",
      "peetres proof",
      "phenomenon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2782W"
    }
  }
}