Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups

Dąbrowski, Damian; Villa, Michele

doi:10.1017/S0305004123000245

dc.contributor.author	Dąbrowski, Damian
dc.contributor.author	Villa, Michele
dc.date.accessioned	2024-02-23T10:59:59Z
dc.date.available	2024-02-23T10:59:59Z
dc.date.issued	2023
dc.identifier.citation	Dąbrowski, D., & Villa, M. (2023). Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, <i>175</i>(2), 445-458. <a href="https://doi.org/10.1017/S0305004123000245" target="_blank">https://doi.org/10.1017/S0305004123000245</a>
dc.identifier.other	CONVID_183585734
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/93636
dc.description.abstract	Let μ be a Radon measure on the nth Heisenberg group Hn. In this note we prove that if the (2n+1) -dimensional (Heisenberg) Riesz transform on Hn is L2(μ) -bounded, and if μ(F)=0 for all Borel sets with dimH(F)≤2 , then μ must have (2n+1) -polynomial growth. This is the Heisenberg counterpart of a result of Guy David from [ Dav91 ].	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Cambridge University Press (CUP)
dc.relation.ispartofseries	Mathematical Proceedings of the Cambridge Philosophical Society
dc.rights	CC BY-NC-ND 4.0
dc.title	Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-202402232102
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	445-458
dc.relation.issn	0305-0041
dc.relation.numberinseries	2
dc.relation.volume	175
dc.type.version	acceptedVersion
dc.rights.copyright	© 2023 Cambridge University Press
dc.rights.accesslevel	openAccess	fi
dc.subject.yso	mittateoria
dc.subject.yso	harmoninen analyysi
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p13386
jyx.subject.uri	http://www.yso.fi/onto/yso/p28124
dc.rights.url	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi	10.1017/S0305004123000245
jyx.fundinginformation	DAMIAN DĄBROWSKI †§ MICHELE VILLA ‡§ † Supported by Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (grant MDM-2014-0445). Partially supported by the Catalan Agency for Management of University and Research Grants (grant 2017-SGR-0395), and by the Spanish Ministry of Science, Innovation and Universities (grant MTM-2016-77635-P). ‡ Supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (grant EP/L016508/01), the Scottish Funding Council, Heriot-Watt University and the University of Edinburgh. § Partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
dc.type.okm	A1