Infinitesimally Lipschitz functions on metric spaces
| dc.contributor.author | Durand-Cartagena, Estibalitz | |
| dc.contributor.author | Jaramillo Aguado, Jesús Ángel | |
| dc.date.accessioned | 2023-06-19T13:28:05Z | |
| dc.date.available | 2023-06-19T13:28:05Z | |
| dc.date.issued | 2013 | |
| dc.description.abstract | For a metric space X, we study the space D∞(X) of bounded functions on X whose infinitesimal Lipschitz constant is uniformly bounded. D∞(X) is compared with the space LIP∞(X) of bounded Lipschitz functions on X, in terms of different properties regarding the geometry of X. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare D∞(X) with the Newtonian-Sobolev space N1,∞(X). In particular, if X supports a doubling measure and satisfies a local Poincaré inequality, we obtain that D∞(X) = N1,∞(X). | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | DGES (Spain) | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28383 | |
| dc.identifier.officialurl | http://arxiv.org/pdf/0901.3236v1.pdf | |
| dc.identifier.relatedurl | http://arxiv.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33788 | |
| dc.journal.title | Preprint | |
| dc.language.iso | eng | |
| dc.relation.projectID | MTM2006-03531 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Infinitesimally Lipschitz functions on metric spaces | |
| dc.type | journal article | |
| dcterms.references | [Am] L. Ambrosio, P. Tilli: Topics on Analysis in Metri Spaces. Oxford Lecture Series in Mathematics and its Applications 25. Oxford University Press, Oxford, (2004). [BRZ] Z. M. Balogh, K. Rogovin, T. Zürcher: The Stepanov Differentiability Theorem in Metric Measure Spaces. J. Geom. Anal. 14 no. 3, (2004), 405–422. [Ch] J. Cheeger: Differentiability of Lipschitz Functions on metric measure spaces. Geom. Funct. Anal. 9 (1999), 428–517. [F] G.B. Folland: Real Analysis, Modern Techniques and Their Applications. Pure and Applied Mathematics (1999). [Fu] B. Fuglede : Extremal length and functional completion. Acta. Math. 98 (1957), 171–219. [GJ1] M. I. Garrido, J. A. Jaramillo: A Banach-Stone Theorem for Uniformly Continuous Functions. Monatshefte für mathematik. 131 (2000), 189–192. [GJ2] M. I. Garrido, J. A. Jaramillo: Homomorphism on Function Lattices. Monatshefte fü mathematik. 141 (2004), 127–146. [GJ3] M. I. Garrido, J. A. Jaramillo: Lipschitz-type functions on metric spaces. J. Math. Anal and Appl. 340 (2008), 282–290. [GiJe] L. Gillman, J. Jerison: Rings of Continuous Functions. Springer-Verlag, New-York (1976). [Ha1] P. Haj lasz: Sobolev spaces on metric-measure spaces. Contemp. Math. 338 (2003), 173–218. [Ha2] P. Haj lasz: Sobolev spaces on an arbitrary metric space. Potential Anal. 5 (1996), 403–415. [He1] J. Heinonen: Lectures on Analysis on Metric Spaces. Springer (2001). [He2] J. Heinonen: Nonsmooth calculus. Bull. Amer. Math. Soc. 44 (2007), 163–232. [HK] J. Heinonen, P. Koskela: Quasiconformal maps on metric spaces with controlled geometry. Acta Math. 181 (1998), 1–61. [I] J. R. Isbell: Algebras of uniformly continuous functions. Ann. Math. 68 (1958), 96–125. [JJRRS] E. Järvenp¨a¨a, M. Järvenp¨a¨a, N. Shanmugalingam K. Rogovin, and S. Rogovin: Measurability of equivalence classes and MECp-property in metric spaces. Rev. Mat. Iberoamericana 23 (2007), 811–830. [KMc] P. Koskela, P. MacManus: Quasiconformal mappings and Sobolev spaces. Studia Math. 131 (1998), 1–17. [K] S. Keith: A differentiable structure for metric measure spaces. Adv. Math. 183 (2004), 271–315. [Ma] V. Magnani: Elements of Geometric Measure Theory on sub-Riemannian groups, (2002). Dissertation. Scuola Normale Superiore di Pisa. [M] P. Mattila: Geometry of Sets and Measures in Euclidean Spaces: Fractals and recti-fiability. Cambridge studies in Advance Mathematics, Cambridge University Press 44 (1995). [Me] R. E. Megginson, R. E.: An introduction to Banac Space Theory. Graduate Texts in Mathematics, 183. Springer-Verlag, New York , 1998. [S] S. Semmes: Some Novel Types of Fractal Geometry. Oxford Science Publications (2001). [Sh1] 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. [Sh2] N. Shanmugalingam: Newtonian Spaces: An extension of Sobolev spaces to Metric Measure Spaces. Rev. Mat. Iberoamericana, 16 (2000), 243–279. [W] N. Weaver: Lipschitz Algebras. Singapore: World Scientific (1999) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8b6e753b-df15-44ff-8042-74de90b4e3e9 | |
| relation.isAuthorOfPublication.latestForDiscovery | 8b6e753b-df15-44ff-8042-74de90b4e3e9 |
Download
Original bundle
1 - 1 of 1
