{
  "id": "2010.04034",
  "version": "v1",
  "published": "2020-10-08T14:59:48.000Z",
  "updated": "2020-10-08T14:59:48.000Z",
  "title": "The Green function with pole at infinity applied to the study of the elliptic measure",
  "authors": [
    "Joseph Feneuil"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In $\\mathbb R^{d+1}_+$ or in $\\mathbb R^n\\setminus \\mathbb R^d$ ($d<n-1$), we study the Green function with pole at infinity introduced by David, Engelstein, and Mayboroda. In two cases, we deduce the equivalence between the elliptic measure and the Lebesgue measure on $\\mathbb R^d$; and we further prove the $A_\\infty$-absolute continuity of the elliptic measure for operators that can be related to the two previous cases via Carleson measures, extending the range of operators for which the $A_\\infty$-absolute continuity of the elliptic measure is known.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-08T14:59:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B37",
      "31B25",
      "35J25",
      "35J70"
    ],
    "keywords": [
      "elliptic measure",
      "green function",
      "absolute continuity",
      "carleson measures",
      "lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}