dc.contributor.author | Koskela, Pekka | |
dc.contributor.author | Xiao, Jie | |
dc.contributor.author | Zhang, Yi Ru-Ya | |
dc.contributor.author | Zhou, Yuan | |
dc.date.accessioned | 2019-02-20T13:17:30Z | |
dc.date.available | 2019-02-20T13:17:30Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Koskela, P., Xiao, J., Zhang, Y. R.-Y., & Zhou, Y. (2017). A quasiconformal composition problem for the Q-spaces. <i>Journal of the European Mathematical Society</i>, <i>19</i>(4), 1159-1187. <a href="https://doi.org/10.4171/JEMS/690" target="_blank">https://doi.org/10.4171/JEMS/690</a> | |
dc.identifier.other | CONVID_26960719 | |
dc.identifier.other | TUTKAID_73550 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/62903 | |
dc.description.abstract | Given 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.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | EMS Publishing House | |
dc.relation.ispartofseries | Journal of the European Mathematical Society | |
dc.rights | In Copyright | |
dc.subject.other | quasiconformal mappings | |
dc.subject.other | compositions | |
dc.subject.other | Q-spaces | |
dc.title | A quasiconformal composition problem for the Q-spaces | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-201902181565 | |
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 | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.date.updated | 2019-02-18T16:15:28Z | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 1159-1187 | |
dc.relation.issn | 1435-9855 | |
dc.relation.numberinseries | 4 | |
dc.relation.volume | 19 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © 2019 EMS Publishing House | |
dc.rights.accesslevel | openAccess | fi |
dc.format.content | fulltext | |
dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
dc.relation.doi | 10.4171/JEMS/690 | |