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

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


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.

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Ministry reporting: Yes

Reporting Year: 2021

Preliminary JUFO rating: 2

Last updated on 2021-09-08 at 12:09