{
  "id": "1703.07674",
  "version": "v1",
  "published": "2017-03-22T14:34:48.000Z",
  "updated": "2017-03-22T14:34:48.000Z",
  "title": "Traces of Besov spaces revisited",
  "authors": [
    "Jon Johnsen"
  ],
  "comment": "15 pages. Accepted version. The final version appeared in 2000 in Journal of analysis and applications (at http://dx.doi.org/10.4171/ZAA/979)",
  "journal": "Journal for analysis and its applications, vol. 19 (2000), no. 3, 763--779",
  "doi": "10.4171/ZAA/979",
  "categories": [
    "math.AP"
  ],
  "abstract": "For the trace of Besov spaces $B^s_{p,q}$ onto a hyperplane, the borderline case with $s=\\frac{n}{p}-(n-1)$ and $0<p<1$ is analysed and a new dependence on the sum-exponent $q$ is found. Through examples the restriction operator defined for $s$ down to $1/p$, and valued in $L_p$, is shown to be distinctly different and, moreover, unsuitable for elliptic boundary problems. All boundedness properties (both new and previously known) are found to be easy consequences of a simple mixed-norm estimate, which also yields continuity with respect to the normal coordinate. The surjectivity for the classical borderline $s=\\frac1p$ ($1\\le p<\\infty$) is given a simpler proof for all $q\\in\\,]0,1]$, using only basic functional analysis. The new borderline results are based on corresponding convergence criteria for series with spectral conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-22T14:34:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "besov spaces",
      "elliptic boundary problems",
      "simple mixed-norm estimate",
      "basic functional analysis",
      "boundedness properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}