{
  "id": "1501.02493",
  "version": "v1",
  "published": "2015-01-11T20:33:43.000Z",
  "updated": "2015-01-11T20:33:43.000Z",
  "title": "Traces for Besov spaces on fractal h-sets and dichotomy results",
  "authors": [
    "António Caetano",
    "Dorothee Haroske"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the existence of traces of Besov spaces on fractal $h$-sets $\\Gamma$ with the special focus laid on necessary assumptions implying this existence, or, in other words, present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of [Br4] and a continuation of the recent paper [Ca2]. Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that -- depending on the function space and the set $\\Gamma$ -- there occurs an alternative: either the trace on $\\Gamma$ exists, or smooth functions compactly supported outside $\\Gamma$ are dense in the space. This notion was introduced by Triebel in [Tr7] for the special case of $d$-sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-11T20:33:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "28A80"
    ],
    "keywords": [
      "besov spaces",
      "dichotomy results",
      "fractal h-sets",
      "function space",
      "smooth functions compactly supported outside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}