dc.creator | Lu, Guozhen | es |
dc.creator | Pérez Moreno, Carlos | es |
dc.date.accessioned | 2016-11-14T10:49:16Z | |
dc.date.available | 2016-11-14T10:49:16Z | |
dc.date.issued | 2002-01 | |
dc.identifier.citation | Lu, 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.issn | 1439-8516 | es |
dc.identifier.issn | 1439-7617 | es |
dc.identifier.uri | http://hdl.handle.net/11441/48523 | |
dc.description.abstract | Given 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.sponsorship | National Science Foundation | es |
dc.description.sponsorship | Dirección General de Investigación Científica y Técnica | es |
dc.description.sponsorship | North Atlantic Treaty Organization | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Springer | es |
dc.relation.ispartof | Acta Mathematica Sinica, 18 (1), 1-20. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Sobolev spaces | es |
dc.subject | Representation formulas | es |
dc.subject | High-order derivatives | es |
dc.subject | Vector fields | es |
dc.subject | Metric spaces | es |
dc.subject | Polynomials | es |
dc.subject | Doubling measures | es |
dc.subject | Poincaré inequalities | es |
dc.title | L1 → Lq Poincaré inequalities for 0 < q < 1 imply representation formulas | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | DMS96-22996 | es |
dc.relation.projectID | DMS99-70352 | es |
dc.relation.projectID | PB940192 | es |
dc.relation.projectID | 972144 | es |
dc.relation.publisherversion | https://dx.doi.org/10.1007/s101140100154 | es |
dc.identifier.doi | 10.1007/s101140100154 | es |
dc.contributor.group | Universidad de Sevilla. FQM354: Análisis Real | es |
idus.format.extent | 23 p. | es |
dc.journaltitle | Acta Mathematica Sinica | es |
dc.publication.volumen | 18 | es |
dc.publication.issue | 1 | es |
dc.publication.initialPage | 1 | es |
dc.publication.endPage | 20 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/48523 | |