On arithmetic sums of Ahlfors-regular sets

Orponen, Tuomas

doi:10.1007/s00039-021-00589-x

dc.contributor.author	Orponen, Tuomas
dc.date.accessioned	2022-01-18T13:43:40Z
dc.date.available	2022-01-18T13:43:40Z
dc.date.issued	2022
dc.identifier.citation	Orponen, T. (2022). On arithmetic sums of Ahlfors-regular sets. <i>Geometric and Functional Analysis</i>, <i>32</i>(1), 81-134. <a href="https://doi.org/10.1007/s00039-021-00589-x" target="_blank">https://doi.org/10.1007/s00039-021-00589-x</a>
dc.identifier.other	CONVID_103881631
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/79405
dc.description.abstract	Let A,B⊂RA,B⊂R be closed Ahlfors-regular sets with dimensions dimHA=:αdimH⁡A=:α and dimHB=:βdimH⁡B=:β. I prove that dimH[A+θB]≥α+β⋅1−α2−αdimH⁡[A+θB]≥α+β⋅1−α2−α for all θ∈R∖Eθ∈R∖E, where dimHE=0dimH⁡E=0.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Birkhäuser
dc.relation.ispartofseries	Geometric and Functional Analysis
dc.rights	CC BY 4.0
dc.subject.other	Ahlfors-regular sets
dc.subject.other	sum-product problem
dc.subject.other	Hausdorff dimension
dc.title	On arithmetic sums of Ahlfors-regular sets
dc.type	research article
dc.identifier.urn	URN:NBN:fi:jyu-202201181174
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	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	81-134
dc.relation.issn	1016-443X
dc.relation.numberinseries	1
dc.relation.volume	32
dc.type.version	publishedVersion
dc.rights.copyright	© 2022 the Authors
dc.rights.accesslevel	openAccess	fi
dc.type.publication	article
dc.subject.yso	aritmetiikka
dc.subject.yso	mittateoria
dc.subject.yso	kombinatoriikka
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p3159
jyx.subject.uri	http://www.yso.fi/onto/yso/p13386
jyx.subject.uri	http://www.yso.fi/onto/yso/p4745
dc.rights.url	https://creativecommons.org/licenses/by/4.0/
dc.relation.doi	10.1007/s00039-021-00589-x
jyx.fundinginformation	T.O. is supported by the Academy of Finland via the projects Quantitative rectifiability in Euclidean and non-Euclidean spaces and Incidences on Fractals, grant Nos. 309365, 314172, 321896. T.O. is also supported by the University of Helsinki via the project Quantitative rectifiability of sets and measures in Euclidean spaces and Heisenberg groups, project No. 7516125.
dc.type.okm	A1