A1 Journal article (refereed)
Uniform rectifiability and ε-approximability of harmonic functions in Lp (2020)
Hofmann, S., & Tapiola, O. (2020). Uniform rectifiability and ε-approximability of harmonic functions in Lp. Annales de l'Institut Fourier, 70(4), 1595-1638. https://doi.org/10.5802/aif.3359
JYU authors or editors
Publication details
All authors or editors: Hofmann, Steve; Tapiola, Olli
Journal or series: Annales de l'Institut Fourier
ISSN: 0373-0956
eISSN: 1777-5310
Publication year: 2020
Publication date: 15/04/2021
Volume: 70
Issue number: 4
Pages range: 1595-1638
Publisher: Centre Mersenne; l'Institut Fourier,
Publication country: France
Publication language: English
DOI: https://doi.org/10.5802/aif.3359
Publication open access: Openly available
Publication channel open access: Open Access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/76515
Publication is parallel published: https://arxiv.org/abs/1710.05528
Abstract
Suppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that pointwise, L∞ and Lp type ε-approximability properties of harmonic functions are all equivalent and they characterize uniform rectifiability for codimension 1 Ahlfors–David regular sets. Our results and techniques are generalizations of recent works of T. Hytönen and A. Rosén and the first author, J. M. Martell and S. Mayboroda.
Keywords: harmonic analysis (mathematics); potential theory; measure theory
Free keywords: ε-approximability; uniform rectifiability; Carleson measures; harmonic functions.
Contributing organizations
Related projects
- Centre of Excellence in Analysis and Dynamics Research
- Koskela, Pekka
- Research Council of Finland
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 2