{
  "id": "2410.07773",
  "version": "v1",
  "published": "2024-10-10T10:01:36.000Z",
  "updated": "2024-10-10T10:01:36.000Z",
  "title": "Potential theory and boundary behavior in the Drury-Arveson space",
  "authors": [
    "Nikolaos Chalmoukis",
    "Michael Hartz"
  ],
  "comment": "40 pages",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We develop a notion of capacity for the Drury-Arveson space $H^2_d$ of holomorphic functions on the Euclidean unit ball. We show that every function in $H^2_d$ has a non-tangential limit (in fact Kor\\'anyi limit) at every point in the sphere outside of a set of capacity zero. Moreover, we prove that the capacity zero condition is sharp, and that it is equivalent to being totally null for $H^2_d$. We also provide applications to cyclicity. Finally, we discuss generalizations of these results to other function spaces on the ball.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-10T10:01:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22",
      "31B15",
      "32U20"
    ],
    "keywords": [
      "drury-arveson space",
      "boundary behavior",
      "potential theory",
      "euclidean unit ball",
      "capacity zero condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}