{
  "id": "2202.07898",
  "version": "v1",
  "published": "2022-02-16T07:04:11.000Z",
  "updated": "2022-02-16T07:04:11.000Z",
  "title": "Weighted estimates for bilinear fractional integral operator on the Heisenberg group",
  "authors": [
    "Abhishek Ghosh",
    "Rajesh K. Singh"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this article, we introduce an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group $\\mathbb{H}^n$. We completely characterize exponents $\\alpha, \\beta$ and $\\gamma$ such that the operator is bounded from $L^{p}(\\mathbb{H}^n, |x|^{\\alpha p})\\times L^{q}(\\mathbb{H}^n, |x|^{\\beta q})$ to $L^{r}(\\mathbb{H}^n, |x|^{-\\gamma r})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-16T07:04:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg group",
      "weighted estimates",
      "steins bilinear fractional integral operator",
      "characterize exponents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}