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Lipschitz continuity for weighted harmonic functions in the unit disc

Olofsson, Anders LU (2020) In Complex Variables and Elliptic Equations 65(10). p.1630-1660
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.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
D. Khavinson, Fourier multiplier, harmonic function, Lipschitz continuity, Poisson integral, Primary: 31A05, Secondary: 35J25
in
Complex Variables and Elliptic Equations
volume
65
issue
10
pages
31 pages
publisher
Taylor & Francis
external identifiers
  • scopus:85073994292
ISSN
1747-6933
DOI
10.1080/17476933.2019.1669572
language
English
LU publication?
yes
id
eda287eb-1c4e-4809-8f6c-9ae0e9a3197b
date added to LUP
2019-11-06 13:27:49
date last changed
2022-04-18 18:40:39
@article{eda287eb-1c4e-4809-8f6c-9ae0e9a3197b,
  abstract     = {{<p>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.</p>}},
  author       = {{Olofsson, Anders}},
  issn         = {{1747-6933}},
  keywords     = {{D. Khavinson; Fourier multiplier; harmonic function; Lipschitz continuity; Poisson integral; Primary: 31A05; Secondary: 35J25}},
  language     = {{eng}},
  number       = {{10}},
  pages        = {{1630--1660}},
  publisher    = {{Taylor & Francis}},
  series       = {{Complex Variables and Elliptic Equations}},
  title        = {{Lipschitz continuity for weighted harmonic functions in the unit disc}},
  url          = {{http://dx.doi.org/10.1080/17476933.2019.1669572}},
  doi          = {{10.1080/17476933.2019.1669572}},
  volume       = {{65}},
  year         = {{2020}},
}