{
  "id": "1606.06749",
  "version": "v1",
  "published": "2016-06-21T20:05:04.000Z",
  "updated": "2016-06-21T20:05:04.000Z",
  "title": "On Whitney-type problem for weighted Sobolev spaces on $d$-thick closed sets",
  "authors": [
    "A. I. Tyulenev",
    "S. K. Vodop'yanov"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A~complete intrinsic description of the traces of weighted Sobolev space $W^{l}_{p}(\\mathbb{R}^{n}, \\gamma)$ on~$d$-thick closed weakly regular subsets $F$ of~$\\mathbb{R}^{n}$ with $\\gamma \\in A_{\\frac{p}{r}}(\\mathbb{R}^{n})$, $p \\in (1,\\infty)$, $r \\in (\\max\\{1,n-d\\},p)$, $l \\in \\mathbb{N}$, $0 < d \\le n$, is given. The results obtained supplement, on one side, the studies of P.~Shvartsman, who described in~\\cite{Shv2}, the traces of the spaces $W^{1}_{p}(\\mathbb{R}^{n})$, $p > n$, on arbitrary closed sets, and in~\\cite{Shv1}, the traces of the Besov and Lizorkin--Triebel spaces on Ahlfors regular closed subsets of $\\mathbb{R}^{n}$ with $l \\in \\mathbb{N}$, $p \\in (1,\\infty)$. On the other side, our result supplement the results of V.\\,S.~Rychkov~\\cite{Ry2}, who described the traces of Sobolev spaces on $d$-thick sets under the condition $d > n-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-21T20:05:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted sobolev space",
      "thick closed sets",
      "whitney-type problem",
      "thick closed weakly regular subsets",
      "ahlfors regular closed subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}