Lipschitz continuity for weighted harmonic functions in the unit disc

Research output: Contribution to journalArticle

Abstract

We study membership in Lipschitz classes (Formula presented.) for a class of α-harmonic functions in the open unit disc (Formula presented.) in the complex plane. From earlier work by Olofsson and Wittsten we know that such an α-harmonic function u is the α-harmonic Poisson integral (Formula presented.) of its boundary value function f on the unit circle (Formula presented.). We determine when the Poisson integral (Formula presented.) belongs to a Lipschitz class (Formula presented.) for the unit disc.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • D. Khavinson, Fourier multiplier, harmonic function, Lipschitz continuity, Poisson integral, Primary: 31A05, Secondary: 35J25
Original languageEnglish
Pages (from-to)1630-1660
Number of pages31
JournalComplex Variables and Elliptic Equations
Volume65
Issue number10
Early online date2019 Sep 27
Publication statusPublished - 2020
Publication categoryResearch
Peer-reviewedYes