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dc.creatorLu, Guozhenes
dc.creatorPérez Moreno, Carloses
dc.date.accessioned2016-11-14T10:49:16Z
dc.date.available2016-11-14T10:49:16Z
dc.date.issued2002-01
dc.identifier.citationLu, G. y Pérez Moreno, C. (2002). L1 → Lq Poincaré inequalities for 0 < q < 1 imply representation formulas. Acta Mathematica Sinica, 18 (1), 1-20.
dc.identifier.issn1439-8516es
dc.identifier.issn1439-7617es
dc.identifier.urihttp://hdl.handle.net/11441/48523
dc.description.abstractGiven two doubling measures μ and ν in a metric space (S, ρ) of homogeneous type, let B0⊂S be a given ball. It has been a well-known result by now (see [1–4]) that the validity of an L1→L1 Poincaré inequality of the following form: ∫B|f−fB|dv⩽cr(B)∫Bgdμ, for all metric balls B⊂B0⊂S, implies a variant of representation formula of fractional integral type: for ν-a.e. x∈B0, |f(x)−fB0|⩽C∫B0g(y)ρ(x,y)μ(B(x,ρ(x,y)))dμ(y)+Cr(B0)μ(B0)∫B0g(y)dμ(y). One of the main results of this paper shows that an L1 to Lq Poincaré inequality for some 0 < q < 1, i.e., (∫B|f−fB|qdv)1/q⩽cr(B)∫Bgdμ, for all metric balls B⊂B0, will suffice to imply the above representation formula. As an immediate corollary, we can show that the weak-type condition, supλ>0λν({x∈B:|f(x)−fB|>λ})ν(B)⩽Cr(B)∫Bgdμ, also implies the same formula. Analogous theorems related to high-order Poincaré inequalities and Sobolev spaces in metric spaces are also proved.es
dc.description.sponsorshipNational Science Foundationes
dc.description.sponsorshipDirección General de Investigación Científica y Técnicaes
dc.description.sponsorshipNorth Atlantic Treaty Organizationes
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherSpringeres
dc.relation.ispartofActa Mathematica Sinica, 18 (1), 1-20.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectSobolev spaceses
dc.subjectRepresentation formulases
dc.subjectHigh-order derivativeses
dc.subjectVector fieldses
dc.subjectMetric spaceses
dc.subjectPolynomialses
dc.subjectDoubling measureses
dc.subjectPoincaré inequalitieses
dc.titleL1 → Lq Poincaré inequalities for 0 < q < 1 imply representation formulases
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/submittedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Análisis Matemáticoes
dc.relation.projectIDDMS96-22996es
dc.relation.projectIDDMS99-70352es
dc.relation.projectIDPB940192es
dc.relation.projectID972144es
dc.relation.publisherversionhttps://dx.doi.org/10.1007/s101140100154es
dc.identifier.doi10.1007/s101140100154es
dc.contributor.groupUniversidad de Sevilla. FQM354: Análisis Reales
idus.format.extent23 p.es
dc.journaltitleActa Mathematica Sinicaes
dc.publication.volumen18es
dc.publication.issue1es
dc.publication.initialPage1es
dc.publication.endPage20es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/48523

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