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dc.contributor.authorHeikkinen, Toni
dc.contributor.authorKoskela, Pekka
dc.contributor.authorTuominen, Heli
dc.date.accessioned2017-02-28T10:05:43Z
dc.date.available2017-02-28T10:05:43Z
dc.date.issued2017
dc.identifier.citationHeikkinen, T., Koskela, P., & Tuominen, H. (2017). Approximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions. <i>Transactions of the American Mathematical Society</i>, <i>369</i>(5), 3547-3573. <a href="https://doi.org/10.1090/tran/6886" target="_blank">https://doi.org/10.1090/tran/6886</a>
dc.identifier.otherCONVID_26415576
dc.identifier.otherTUTKAID_72270
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/53140
dc.description.abstractWe show that, for 0 < s < 1, 0 < p, q < ∞, Haj lasz–Besov and Haj lasz–Triebel–Lizorkin functions can be approximated in the norm by discrete median convolutions. This allows us to show that, for these functions, the limit of medians, lim r→0 mγ u (B(x, r)) = u ∗ (x), exists quasieverywhere and defines a quasicontinuous representative of u. The above limit exists quasieverywhere also for Haj lasz functions u ∈ Ms,p, 0 < s ≤ 1, 0 < p < ∞, but approximation of u in Ms,p by discrete (median) convolutions is not in general possible.
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.relation.ispartofseriesTransactions of the American Mathematical Society
dc.relation.urihttp://www.ams.org/journals/tran/0000-000-00/S0002-9947-2016-06886-5/S0002-9947-2016-06886-5.pdf
dc.subject.otherBesov space
dc.subject.otherTriebel–Lizorkin space
dc.subject.otherfractional Sobolev space
dc.subject.othermetric measure space
dc.subject.othermedian
dc.subject.otherquasicontinuity
dc.titleApproximation and Quasicontinuity of Besov and Triebel–Lizorkin Functions
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201702131428
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2017-02-13T13:15:27Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange3547-3573
dc.relation.issn0002-9947
dc.relation.numberinseries5
dc.relation.volume369
dc.type.versionacceptedVersion
dc.rights.copyright© 2016 American Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by AMS. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1090/tran/6886
dc.type.okmA1


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