Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞
| dc.contributor.author | Durand-Cartagena, Estibalitz | |
| dc.contributor.author | Jaramillo Aguado, Jesús Ángel | |
| dc.contributor.author | Shanmugalingam, Nageswari | |
| dc.date.accessioned | 2023-06-20T03:48:05Z | |
| dc.date.available | 2023-06-20T03:48:05Z | |
| dc.date.issued | 2009-10 | |
| dc.description.abstract | We study a geometric characterization of ∞−Poincaré inequality. We show that a path-connected complete doubling metric measure space supports an ∞−Poincaré inequality if and only if it is thick quasi-convex. We also prove that these two equivalent properties are also equivalent to the purely analytic property that N1,∞(X) = LIP∞(X), where LIP∞(X) is the collection of bounded Lipschitz functions on X and N1,∞(X) is the Newton-Sobolev space studied in [DJ]. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28477 | |
| dc.identifier.officialurl | http://www.recercat.cat/bitstream/handle/2072/47933/Pr895.pdf?sequence=1 | |
| dc.identifier.relatedurl | http://www.crm.cat/en/Pages/default.aspx | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/44466 | |
| dc.issue.number | 895 | |
| dc.journal.title | Prepublicacions del Centre de Recerca Matemàtica | |
| dc.language.iso | eng | |
| dc.publisher | Centre de Recerca Matemàtica | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞ | |
| dc.type | journal article | |
| dcterms.references | S. G. Bobkov, C. Houdre: Some connections between isoperimetric and Sobolev-type inequalities. (English summary) Mem. Amer. Math. Soc. 129 (616) (1997). M. Bourdon, H. Pajot Quasi-conformal geometry and hyperbolic geometry. (English summary) Rigidity in dynamics and geometry (Cambridge, 2000), 1–17, Springer, Berlin, 2002. E. Durand, J. A. Jaramillo: Pointwise Lipschitz functions on metric spaces. To appear in J. Math. Anal. Appl. (2009). G.B. Folland: Real Analysis, Modern Techniques and Their Applications. Pure and Applied Mathematics (1999). P. Hajlasz: Sobolev spaces on metric-measure spaces. Contemp. Math. 338 (2003), 173–218. P. Hajlasz, P. Koskela: Sobolev met Poincaré. (English summary) Mem. Amer. Math. Soc. 145(668) (2000). J. Heinonen, P. Koskela: A note on Lipschitz Functions, Upper Gradients, and the Poincaré Inequality. New Zealand J. Math. 28 (1999), 37–42. J. Heinonen, P. Koskela: Quasiconformal maps in metric spaces with controlled geometry. Acta Math. 181 (1998), 1–61. E. Järvenpää, M. Järvenpää, N. Shanmugalingam K. Rogovin, and S. Rogovin: Measurability of equivalence classes and MECp−property in metric spaces. Rev. Mat. Iberoamericana 23 (2007), 811–830. J. Kinnunen, R. Korte: Characterizations of Sobolev inequalities on metric spaces. J. Math. Anal. Appl. 344 (2008), 1093–1104. R. Korte: Geometric implications of the Poincaré inequality, Licentiate’s thesis, Helsinki University of Technology, 2006. M. Miranda: Functions of bounded variation on “good” metric spaces. J. Math. Pures Appl. (9) 83 (2003), 975–1004. S. Semmes: Some Novel Types of Fractal Geometry. Oxford Science Publications (2001). S.Semmes: Finding Curves on General Spaces through Quantitative Topology, with Applications to Sobolev and Poincaré Inequalities. Selecta Math., New Series 2(2) (1996), 155–295 N. Shanmugalingam: “Newtonian Spaces: An extension of Sobolev spaces to Metric Measure Spaces” Ph. D. Thesis, University of Michigan (1999), http: math.uc.edu/~nages/papers.html. N. Shanmugalingam: Newtonian Spaces: An extension of Sobolev spaces to Metric Measure Spaces. Rev. Mat. Iberoamericana, 16 (2000), 243–279. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8b6e753b-df15-44ff-8042-74de90b4e3e9 | |
| relation.isAuthorOfPublication.latestForDiscovery | 8b6e753b-df15-44ff-8042-74de90b4e3e9 |
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