Uniform rectifiability and ε-approximability of harmonic functions in Lp

Hofmann, Steve; Tapiola, Olli

doi:10.5802/aif.3359

dc.contributor.author	Hofmann, Steve
dc.contributor.author	Tapiola, Olli
dc.date.accessioned	2021-06-14T12:08:48Z
dc.date.available	2021-06-14T12:08:48Z
dc.date.issued	2020
dc.identifier.citation	Hofmann, S., & Tapiola, O. (2020). Uniform rectifiability and ε-approximability of harmonic functions in Lp. <i>Annales de l'Institut Fourier</i>, <i>70</i>(4), 1595-1638. <a href="https://doi.org/10.5802/aif.3359" target="_blank">https://doi.org/10.5802/aif.3359</a>
dc.identifier.other	CONVID_97818425
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/76515
dc.description.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.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Centre Mersenne; l'Institut Fourier,
dc.relation.ispartofseries	Annales de l'Institut Fourier
dc.rights	CC BY-ND 4.0
dc.subject.other	ε-approximability
dc.subject.other	uniform rectifiability
dc.subject.other	Carleson measures
dc.subject.other	harmonic functions.
dc.title	Uniform rectifiability and ε-approximability of harmonic functions in Lp
dc.type	research article
dc.identifier.urn	URN:NBN:fi:jyu-202106143717
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Analyysin ja dynamiikan tutkimuksen huippuyksikkö	fi
dc.contributor.oppiaine	Mathematics	en
dc.contributor.oppiaine	Analysis and Dynamics Research (Centre of Excellence)	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	1595-1638
dc.relation.issn	0373-0956
dc.relation.numberinseries	4
dc.relation.volume	70
dc.type.version	publishedVersion
dc.rights.copyright	© 2020 Association des Annales de l’institut Fourier
dc.rights.accesslevel	openAccess	fi
dc.type.publication	article
dc.relation.grantnumber	307333 HY
dc.subject.yso	harmoninen analyysi
dc.subject.yso	mittateoria
dc.subject.yso	potentiaaliteoria
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p28124
jyx.subject.uri	http://www.yso.fi/onto/yso/p13386
jyx.subject.uri	http://www.yso.fi/onto/yso/p18911
dc.rights.url	https://creativecommons.org/licenses/by-nd/4.0/
dc.relation.doi	10.5802/aif.3359
dc.relation.funder	Research Council of Finland	en
dc.relation.funder	Suomen Akatemia	fi
jyx.fundingprogram	Centre of Excellence, AoF	en
jyx.fundingprogram	Huippuyksikkörahoitus, SA	fi
jyx.fundinginformation	S.H. was supported by NSF grant DMS-1664047. O.T. was supported by Emil Aaltosen Säätiö through Foundations’ Post Doc Pool grant. In the previous stages of this work, he was supported by the European Union through T. Hytönen’s ERC Starting Grant 278558 “Analytic-probabilistic methods for borderline singular integrals” and the Finnish Centre of Excellence in Analysis and Dynamics Research.
dc.type.okm	A1