{
  "id": "2002.01917",
  "version": "v1",
  "published": "2020-02-05T18:45:11.000Z",
  "updated": "2020-02-05T18:45:11.000Z",
  "title": "$L^p$ regularity for a class of averaging operators on the Heisenberg group",
  "authors": [
    "Geoffrey Bentsen"
  ],
  "comment": "28 Pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove $L^p_{comp}\\to L^p_{s}$ boundedness for averaging operators associated to a class of curves in the Heisenberg group $\\mathbb{H}^1$ via $L^2$ estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all $L^p$ functions boundedly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-05T18:45:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "44A12",
      "42B20",
      "42B35",
      "46E35"
    ],
    "keywords": [
      "heisenberg group",
      "regularity",
      "bourgain-demeter decoupling inequalities",
      "sobolev space",
      "averaging operators map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}