{
  "id": "1210.3564",
  "version": "v1",
  "published": "2012-10-12T16:20:39.000Z",
  "updated": "2012-10-12T16:20:39.000Z",
  "title": "A sharp multiplier theorem for Grushin operators in arbitrary dimensions",
  "authors": [
    "Alessio Martini",
    "Detlef Müller"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In a recent work by A. Martini and A. Sikora (arXiv:1204.1159), sharp L^p spectral multiplier theorems for the Grushin operators acting on $R^{d_1} \\times R^{d_2}$ are obtained in the case $d_1 \\geq d_2$. Here we complete the picture by proving sharp results in the case $d_1 < d_2$. Our approach exploits L^2 weighted estimates with \"extra weights\" depending only on the second factor of $R^{d_1} \\times R^{d_2}$ (in contrast with the mentioned work, where the \"extra weights\" depend on the first factor) and gives a new unified proof of the sharp results without restrictions on the dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-12T16:20:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A85",
      "42B15"
    ],
    "keywords": [
      "sharp multiplier theorem",
      "grushin operators",
      "arbitrary dimensions",
      "extra weights",
      "spectral multiplier theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.3564M"
    }
  }
}