{
  "id": "2009.09686",
  "version": "v1",
  "published": "2020-09-21T08:50:46.000Z",
  "updated": "2020-09-21T08:50:46.000Z",
  "title": "Vector-valued Sobolev spaces based on Banach function spaces",
  "authors": [
    "Nikita Evseev"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is known that for Banach valued functions there are several approaches to define a Sobolev class. We compare the usual definition via weak derivatives with the Reshetnyak-Sobolev space and with the Newtonian space; in particular, we provide sufficient conditions when all three agree. As well we revise the difference quotient criterion and the property of Lipschitz mapping to preserve Sobolev space when it acting as a superposition operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-21T08:50:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46E40",
      "46B22"
    ],
    "keywords": [
      "banach function spaces",
      "vector-valued sobolev spaces",
      "preserve sobolev space",
      "difference quotient criterion",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}