{
  "id": "1210.0590",
  "version": "v1",
  "published": "2012-10-01T21:47:06.000Z",
  "updated": "2012-10-01T21:47:06.000Z",
  "title": "Sobolev $L^2_p$-functions on closed subsets of $R^2$",
  "authors": [
    "Pavel Shvartsman"
  ],
  "comment": "109 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For each $p>2$ we give intrinsic characterizations of the restriction of the homogeneous Sobolev space $L^1_p(R^2)$ to an arbitrary finite subset $E$ of $R^2$. The trace criterion is expressed in terms of certain weighted oscillations of the second order with respect to a measure generated by the Menger curvature of triangles with vertices in $E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-01T21:47:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "closed subsets",
      "arbitrary finite subset",
      "homogeneous sobolev space",
      "intrinsic characterizations",
      "trace criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 109,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0590S"
    }
  }
}