dc.contributor.author | Fässler, Katrin | |
dc.contributor.author | Orponen, Tuomas | |
dc.date.accessioned | 2021-08-18T06:02:50Z | |
dc.date.available | 2021-08-18T06:02:50Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Fässler, K., & Orponen, T. (2021). Singular integrals on regular curves in the Heisenberg group. <i>Journal de Mathematiques Pures et Appliquees</i>, <i>153</i>, 30-113. <a href="https://doi.org/10.1016/j.matpur.2021.07.004" target="_blank">https://doi.org/10.1016/j.matpur.2021.07.004</a> | |
dc.identifier.other | CONVID_99131371 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/77393 | |
dc.description.abstract | Let be the first Heisenberg group, and let be a kernel which is either odd or horizontally odd, and satisfies
The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel . We prove that convolution with k, as above, yields an -bounded operator on regular curves in . This extends a theorem of G. David to the Heisenberg group.
As a corollary of our main result, we infer that all 3-dimensional horizontally odd kernels yield bounded operators on Lipschitz flags in . This is needed for solving sub-elliptic boundary value problems on domains bounded by Lipschitz flags via the method of layer potentials. The details are contained in a separate paper. Finally, our technique yields new results on certain non-negative kernels, introduced by Chousionis and Li. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Elsevier BV | |
dc.relation.ispartofseries | Journal de Mathematiques Pures et Appliquees | |
dc.rights | CC BY 4.0 | |
dc.subject.other | uniform rectifiability | |
dc.subject.other | singular integrals | |
dc.subject.other | Heisenberg group | |
dc.title | Singular integrals on regular curves in the Heisenberg group | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202108184556 | |
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.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 30-113 | |
dc.relation.issn | 0021-7824 | |
dc.relation.volume | 153 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2021 the Authors | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 321696 | |
dc.format.content | fulltext | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1016/j.matpur.2021.07.004 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Academy Research Fellow, AoF | en |
jyx.fundingprogram | Akatemiatutkija, SA | fi |
jyx.fundinginformation | K.F. is supported by the Academy of Finland via the project Singular integrals, harmonic functions, and boundary regularity in Heisenberg groups, grant No. 321696. | |
dc.type.okm | A1 | |