{
  "id": "1507.01211",
  "version": "v1",
  "published": "2015-07-05T12:24:37.000Z",
  "updated": "2015-07-05T12:24:37.000Z",
  "title": "Haar projection numbers and failure of unconditional convergence in Sobolev spaces",
  "authors": [
    "Andreas Seeger",
    "Tino Ullrich"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "For $1<p<\\infty$ we determine the precise range of $L_p$ Sobolev spaces for which the Haar system is an unconditional basis. We also consider the natural extensions to Triebel-Lizorkin spaces and prove upper and lower bounds for norms of projection operators depending on properties of the Haar frequency set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-05T12:24:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46B15",
      "42C40"
    ],
    "keywords": [
      "haar projection numbers",
      "sobolev spaces",
      "unconditional convergence",
      "haar frequency set",
      "unconditional basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150701211S"
    }
  }
}