Lipschitz continuity for weighted harmonic functions in the unit disc
(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.
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- author
- Olofsson, Anders LU
- organization
- publishing date
- 2020
- 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}}, }