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dc.contributor.authorKoskela, Pekka
dc.contributor.authorXiao, Jie
dc.contributor.authorZhang, Yi Ru-Ya
dc.contributor.authorZhou, Yuan
dc.date.accessioned2019-02-20T13:17:30Z
dc.date.available2019-02-20T13:17:30Z
dc.date.issued2017fi
dc.identifier.citationKoskela, P., Xiao, J., Zhang, Y.-Y., & Zhou, Y. (2017). A quasiconformal composition problem for the Q-spaces. <em>Journal of the European Mathematical Society</em>, 19 (4), 1159-1187. <a href="https://doi.org/10.4171/JEMS/690">doi:10.4171/JEMS/690</a>fi
dc.identifier.otherTUTKAID_73550
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/62903
dc.description.abstractGiven a quasiconformal mapping f:Rn→Rn with n≥2, we show that (un-)boundedness of the composition operator Cf on the spaces Qα(Rn) depends on the index α and the degeneracy set of the Jacobian Jf. We establish sharp results in terms of the index α and the local/global self-similar Minkowski dimension of the degeneracy set of Jf. This gives a solution to [3, Problem 8.4] and also reveals a completely new phenomenon, which is totally different from the known results for Sobolev, BMO, Triebel–Lizorkin and Besov spaces. Consequently, Tukia–Väisälä's quasiconformal extension f:Rn→Rn of an arbitrary quasisymmetric mapping g:Rn−p→Rn−p is shown to preserve Qα(Rn) for any (α,p)∈(0,1)×[2,n)∪(0,1/2)×{1}. Moreover, Qα(Rn) is shown to be invariant under inversions for all 0<α<1.fi
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherEMS Publishing House
dc.relation.ispartofseriesJournal of the European Mathematical Society
dc.rightsIn Copyright
dc.subject.otherquasiconformal mappingsfi
dc.subject.othercompositionsfi
dc.subject.otherQ-spacesfi
dc.titleA quasiconformal composition problem for the Q-spacesfi
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201902181565
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikka
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2019-02-18T16:15:28Z
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1159-1187
dc.relation.issn1435-9855
dc.relation.numberinseries4
dc.relation.volume19
dc.type.versionacceptedVersion
dc.rights.copyright© 2019 EMS Publishing House
dc.rights.accesslevelopenAccessfi
dc.format.contentfulltext
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.4171/JEMS/690


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