{
  "id": "2004.11447",
  "version": "v1",
  "published": "2020-04-23T20:16:09.000Z",
  "updated": "2020-04-23T20:16:09.000Z",
  "title": "The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups",
  "authors": [
    "Vasileios Chousionis",
    "Sean Li",
    "Robert Young"
  ],
  "categories": [
    "math.MG",
    "math.CA"
  ],
  "abstract": "We show that the $\\beta$--numbers of intrinsic Lipschitz graphs of Heisenberg groups $\\mathbb{H}_n$ are locally Carleson integrable when $n \\geq 2$. Our technique relies on a recent Dorronsoro inequality \\cite{FO} as well as a novel slicing argument. A key ingredient in our proof is a Euclidean inequality bounding the $\\beta$--number of a function on a cube of $\\mathbb{R}^n$ using the $\\beta$--number of the restriction of the function to codimension--1 slices of the cube.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-23T20:16:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intrinsic lipschitz graphs",
      "strong geometric lemma",
      "heisenberg groups",
      "technique relies",
      "euclidean inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}