{
  "id": "0903.3214",
  "version": "v1",
  "published": "2009-03-18T18:24:04.000Z",
  "updated": "2009-03-18T18:24:04.000Z",
  "title": "Kolmogorov compactness criterion in variable exponent Lebesgue spaces",
  "authors": [
    "Humberto Rafeiro"
  ],
  "comment": "8 pages",
  "journal": "Proc. A. Razmadze Math. Inst. 150 (2009), 105-113.",
  "categories": [
    "math.FA"
  ],
  "abstract": "The well-known Kolmogorov compactness criterion is extended to the case of variable exponent Lebesgue spaces $L^{p(\\cdot)}({\\Omega})$, where $\\Omega$ is a bounded open set in $\\mathbb R^n$ and $p(\\cdot)$ satisfies some \"standard\" conditions. Our final result should be called Kolmogorov-Tulajkov Sudakov compactness criterion, since it includes the case $p_-=1$ and requires only the \"uniform\" condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-18T18:24:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B50",
      "46E30"
    ],
    "keywords": [
      "variable exponent lebesgue spaces",
      "well-known kolmogorov compactness criterion",
      "kolmogorov-tulajkov sudakov compactness criterion",
      "bounded open set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3214R"
    }
  }
}