{
  "id": "2404.18342",
  "version": "v1",
  "published": "2024-04-29T00:53:55.000Z",
  "updated": "2024-04-29T00:53:55.000Z",
  "title": "On the Trace of $W_{a}^{m+1,1}(\\mathbb{R}_{+}^{n+1})$",
  "authors": [
    "Giovanni Leoni",
    "Daniel Spector"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper, we give a simple proof that any function in the Besov space $B^{m-a,1}(\\mathbb{R}^{n})$ can be extended to a function in $W_{a}^{m+1,1}(\\mathbb{R}_{+}^{n+1})$. In particular, utilizing the intrinsic seminorm in $B^{m-a,1}(\\mathbb{R}^{n})$, we show that either a suitably scaled heat extension or the harmonic extension provides one with the desired lifting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-29T00:53:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "harmonic extension",
      "simple proof",
      "besov space",
      "suitably scaled heat extension",
      "intrinsic seminorm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}