{
  "id": "1706.04796",
  "version": "v1",
  "published": "2017-06-15T09:53:48.000Z",
  "updated": "2017-06-15T09:53:48.000Z",
  "title": "On Luzin N-property and uncertainty principle for the Sobolev mappings",
  "authors": [
    "Adele Ferone",
    "Mikhail V. Korobkov",
    "Alba Roviello"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study Luzin N-property with respect to the Hausdorff measures for Sobolev spaces W^k_p(R^n,R^d). We prove that such N-property holds except for one critical dimensional value t_*=n-(k-1)p; for this critical value the N-property fails in general, and we constructed the corresponding nontrivial counterexample (based on the theory of lacunary Fourier series). Nevertheless, this N-property holds if we assume in addition that the highest k-derivatives belongs to the Lorentz space L_{p,1} instead of L_p. We extend these results to the case of fractional Sobolev spaces as well. Also, we establish some Fubini type theorems for $N$-properties and discuss their applications to the Morse--Sard theorem and its recent extensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-15T09:53:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uncertainty principle",
      "sobolev mappings",
      "n-property holds",
      "study luzin n-property",
      "lacunary fourier series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}