{
  "id": "1406.5743",
  "version": "v2",
  "published": "2014-06-22T17:47:27.000Z",
  "updated": "2014-08-27T11:06:02.000Z",
  "title": "On a theorem of M. Cartwright in higher dimensions",
  "authors": [
    "A. Logunov",
    "E. Malinnikova",
    "P. Mozolyako"
  ],
  "comment": "v.2, 18 pages, added references and acknowledgements, some typos removed",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "We consider harmonic functions in the unit ball of $\\mathbb{R}^{n+1}$ that are unbounded near the boundary but can be estimated from above by some (rapidly increasing) radial weight $w$. Our main result gives some conditions on $w$ that guarantee the estimate from below on the harmonic function by a multiple of this weight. In dimension two this reverse estimate was first obtained by M. Cartwright for the case of the power weights, $w_p(z)=(1-|z|)^{-p}$ for $p>1$, and then generalized to a wide class of regular weights by a number of authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-22T17:47:27.000Z",
      "comment": "17 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-27T11:06:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B05",
      "31B25"
    ],
    "keywords": [
      "higher dimensions",
      "cartwright",
      "harmonic function",
      "radial weight",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5743L"
    }
  }
}