{
  "id": "1410.8478",
  "version": "v1",
  "published": "2014-10-30T18:11:29.000Z",
  "updated": "2014-10-30T18:11:29.000Z",
  "title": "Muckenhoupt weights and Lindelöf theorem for harmonic mappings",
  "authors": [
    "David Kalaj"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CV"
  ],
  "abstract": "We extend the result of Lavrentiev which asserts that the harmonic measure and the arc-length measure are $A_\\infty$ equivalent in a chord-arc Jordan domain. By using this result we extend the classical result of Lindel\\\"of to the class of quasiconformal (q.c.) harmonic mappings by proving the following assertion. Assume that $f$ is a quasiconformal harmonic mapping of the unit disk $\\mathbf{U}$ onto a Jordan domain. Then the function $A(z)=\\arg(\\partial_\\varphi(f(z))/z)$ where $z=re^{i\\varphi}$, is well-defined and smooth in $\\mathbf{U}^*=\\{z: 0<|z|<1\\}$ and has a continuous extension to the boundary of the unit disk if and only if the image domain has $C^1$ boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-30T18:11:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic mapping",
      "lindelöf theorem",
      "muckenhoupt weights",
      "unit disk",
      "chord-arc jordan domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.8478K"
    }
  }
}