{
  "id": "2301.11906",
  "version": "v1",
  "published": "2023-01-27T18:44:39.000Z",
  "updated": "2023-01-27T18:44:39.000Z",
  "title": "A sufficient condition for Haar multipliers in Triebel-Lizorkin spaces",
  "authors": [
    "Gustavo Garrigós",
    "Andreas Seeger",
    "Tino Ullrich"
  ],
  "comment": "13 pages, 5 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider Haar multiplier operators $T_m$ acting on Sobolev spaces, and more generally Triebel-Lizorkin spaces $F^s_{p,q}(\\mathbb{R})$, for indices in which the Haar system is not unconditional. When $m$ depends only on the Haar frequency, we give a sufficient condition for the boundedness of $T_m$ in $F^s_{p,q}$, in terms of the variation norms $\\|m\\|_{V_u}$, which is optimal in $u$ (up to endpoints) when $p, q> 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-27T18:44:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46B15",
      "42C40"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "sufficient condition",
      "haar multiplier operators",
      "variation norms",
      "haar frequency"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}