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Lipschitz continuity for weighted harmonic functions in the unit disc

Olofsson, Anders LU (2019) In Complex Variables and Elliptic Equations
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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author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
D. Khavinson, Fourier multiplier, harmonic function, Lipschitz continuity, Poisson integral, Primary: 31A05, Secondary: 35J25
in
Complex Variables and Elliptic Equations
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
2020-01-13 02:30:26
@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},
  language     = {eng},
  month        = {09},
  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},
  year         = {2019},
}