{
  "id": "1507.08114",
  "version": "v1",
  "published": "2015-07-29T12:28:52.000Z",
  "updated": "2015-07-29T12:28:52.000Z",
  "title": "On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates",
  "authors": [
    "Błażej Wróbel"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the existence of a Mihlin-H\\\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The considered multiplier functions are finitely smooth and satisfy an integral condition at infinity. In particular multipliers of compact support are admitted.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-29T12:28:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "42B25",
      "42B15"
    ],
    "keywords": [
      "square function estimates",
      "mihlin-hörmander functional calculus",
      "consequences",
      "continuous square functions build",
      "spectral multipliers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150708114W"
    }
  }
}