Infinitesimally Lipschitz functions on metric spaces

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dc.creatorDurand, E.
dc.creatorJaramillo, J. A.
dc.date2009-01-21
dc.date.accessioned2026-07-07T12:32:32Z
dc.date.available2026-07-07T12:32:32Z
dc.descriptionFor a metric space $X$, we study the space $D^{\infty}(X)$ of bounded functions on $X$ whose infinitesimal Lipschitz constant is uniformly bounded. $D^{\infty}(X)$ is compared with the space $\LIP^{\infty}(X)$ 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 $D^{\infty}(X)$ with the Newtonian-Sobolev space $N^{1, \infty}(X)$. In particular, if $X$ supports a doubling measure and satisfies a local Poincar{é} inequality, we obtain that $D^{\infty}(X)=N^{1, \infty}(X)$.
dc.description28 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0901.3236
dc.identifierhttp://arxiv.org/abs/0901.3236
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216813
dc.subjectMetric Geometry
dc.subject46E15; 46E35
dc.titleInfinitesimally Lipschitz functions on metric spaces
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