Infinitesimally Lipschitz functions on metric spaces
| Autor: | Durand, E., Jaramillo, J. A. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For 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{\'e} inequality, we obtain that $D^{\infty}(X)=N^{1, \infty}(X)$. Comment: 28 pages, 2 figures |
| Databáze: | arXiv |
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