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dc.contributor.authorKinnunen, Juha
dc.contributor.authorKorte, Riikka
dc.contributor.authorLehrbäck, Juha
dc.contributor.authorVähäkangas, Antti
dc.date.accessioned2019-06-28T07:02:34Z
dc.date.available2020-05-03T21:35:14Z
dc.date.issued2019fi
dc.identifier.citationKinnunen, J., Korte, R., Lehrbäck, J., & Vähäkangas, A. (2019). A maximal Function Approach to Two-Measure Poincaré Inequalities. <em>Journal of Geometric Analysis</em>, 29 (2), 1763-1810. <a href="https://doi.org/10.1007/s12220-018-0061-z">doi:10.1007/s12220-018-0061-z</a>fi
dc.identifier.otherTUTKAID_78516
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/64910
dc.description.abstractThis paper extends the self-improvement result of Keith and Zhong in Keith and Zhong (Ann. Math. 167(2):575–599, 2008) to the two-measure case. Our main result shows that a two-measure (p, p)-Poincaré inequality for 1<p<∞ improves to a (p,p−ε) -Poincaré inequality for some ε>0 under a balance condition on the measures. The corresponding result for a maximal Poincaré inequality is also considered. In this case the left-hand side in the Poincaré inequality is replaced with an integral of a sharp maximal function and the results hold without a balance condition. Moreover, validity of maximal Poincaré inequalities is used to characterize the self-improvement of two-measure Poincaré inequalities. Examples are constructed to illustrate the role of the assumptions. Harmonic analysis and PDE techniques are used extensively in the arguments.fi
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSpringer New York
dc.relation.ispartofseriesJournal of Geometric Analysis
dc.rightsIn Copyright
dc.subject.otherpotentiaaliteoriafi
dc.subject.otherfunktionaalianalyysifi
dc.subject.otherepäyhtälötfi
dc.subject.othergeodesic two-measure spacefi
dc.subject.otherPoincaré inequalityfi
dc.subject.otherself-improvementfi
dc.titleA maximal Function Approach to Two-Measure Poincaré Inequalitiesfi
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201906253435
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.updated2019-06-25T12:15:20Z
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1763-1810
dc.relation.issn1050-6926
dc.relation.numberinseries2
dc.relation.volume29
dc.type.versionacceptedVersion
dc.rights.copyright© Mathematica Josephina, Inc. 2018
dc.rights.accesslevelopenAccessfi
dc.format.contentfulltext
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1007/s12220-018-0061-z


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