{
  "id": "2210.14659",
  "version": "v1",
  "published": "2022-10-26T12:17:42.000Z",
  "updated": "2022-10-26T12:17:42.000Z",
  "title": "Maximal estimates for the bilinear Riesz means on Heisenberg groups",
  "authors": [
    "Min Wang",
    "Hua Zhu"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1712.09238",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we investigate the maximal 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 $2\\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 $\\alpha (p_{1},p_{2})$. For obtaining a lower index $\\alpha (p_{1},p_{2})$, we define two important auxiliary operators and investigate their $L^{p}$ estimates,which play a key role in our proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-26T12:17:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A80",
      "42B15",
      "15A15"
    ],
    "keywords": [
      "heisenberg group",
      "maximal estimates",
      "maximal bilinear riesz means",
      "important auxiliary operators",
      "lower index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}