{
  "id": "2003.04019",
  "version": "v1",
  "published": "2020-03-09T10:16:18.000Z",
  "updated": "2020-03-09T10:16:18.000Z",
  "title": "Dyadic representation theorem using smooth wavelets with compact support",
  "authors": [
    "Tuomas Hytönen",
    "Stefanos Lappas"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "The representation of a general Calder\\'on--Zygmund operator in terms of dyadic Haar shift operators first appeared as a tool to prove the $A_2$ theorem, and it has found a number of other applications. In this paper we prove a new dyadic representation theorem by using smooth compactly supported wavelets in place of Haar functions. A key advantage of this is that we achieve a faster decay of the expansion when the kernel of the general Calder\\'on--Zygmund operator has additional smoothness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-09T10:16:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42C40"
    ],
    "keywords": [
      "dyadic representation theorem",
      "smooth wavelets",
      "compact support",
      "general calderon-zygmund operator",
      "dyadic haar shift operators first"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}