{
  "id": "1712.09238",
  "version": "v1",
  "published": "2017-12-26T11:25:59.000Z",
  "updated": "2017-12-26T11:25:59.000Z",
  "title": "Bilinear Riesz means on the Heisenberg group",
  "authors": [
    "Heping Liu",
    "Min Wang"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we investigate the bilinear Riesz means $S^{\\alpha }$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{\\alpha }$ is bounded from $L^{p_{1}}\\times L^{p_{2}}$ into $ L^{p}$ for $1\\leq p_{1}, p_{2}\\leq \\infty $ and $1/p=1/p_{1}+1/p_{2}$ when $ \\alpha $ is large than a suitable smoothness index $\\alpha (p_{1},p_{2})$. There are some essential differences between the Euclidean space and the Heisenberg group for studying the bilinear Riesz means problem. We make use of some special techniques to obtain a lower index $\\alpha (p_{1},p_{2})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-26T11:25:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A80",
      "22E30",
      "42B15",
      "15A15"
    ],
    "keywords": [
      "heisenberg group",
      "bilinear riesz means problem",
      "lower index",
      "special techniques",
      "euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}