Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures
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Autores: A. Eduardo Gatto, José García-Cuerva Abengoza
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 49, Nº 2, 2005, págs. 285-296
- Idioma: inglés
- DOI: 10.5565/publmat_49205_02
- Enlaces
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Resumen
In the setting of a metric measure space $(\mathbb{X}, d, \mu)$ with an $n$-dimensional Radon measure $\mu$, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure $\mu$ on Lipschitz spaces on the support of $\mu$. Also, for the Euclidean space $\mathbb{R}^d$ with an arbitrary Radon measure $\mu$, we give several characterizations of Lipschitz spaces on the support of $\mu$, $\mathcal{L}ip(\alpha, \mu)$, in terms of mean oscillations involving $\mu$. This allows us to view the "regular" $\mathit{BMO}$ space of X. Tolsa as a limit case for $\alpha\to 0$ of the spaces $\mathcal{L}ip(\alpha, \mu)$.
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