## Abstract

We study the rate at which a positive superharmonic function u can tend to zero at a boundary point z
_{0}of a plane domain G. In particular, if G is a quasidisk, and a > 0 is given, we show that the condition that lim inf «(z)/dist (z, dG)
^{llct}> 0 as z -* z
_{0}in G for any such u is related to the condition that the conformal map/of the unit disk onto G withal) = z
_{0}is Holder continuous with exponent a at the point 1. This leads us to consider the problem of finding the best exponent a for which /is Holder continuous. The answer depends on how we characterize quasidisks or quasicircles. In this connection we give a negative answer to a question of Nakki and Palka.

Original language | English (US) |
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Pages (from-to) | 256-270 |

Number of pages | 15 |

Journal | Journal of the London Mathematical Society |

Volume | s2-39 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1989 |

Externally published | Yes |