Lipschitz spaces and Calderon-Zygmund operators associated to non-doubling measures

Abstract

In the setting of ${\mathbb{R}}^d$ with an $n-$dimensional measure $\mu ,$ we give several characterizations of Lipschitz spaces in terms of mean oscillations involving $\mu .$ We also show that Lipschitz spaces are preserved by those Calderon-Zygmund operators $T$ associated to the measure $\mu$ for which T(1) is the Lipschitz class $0.$

10 pages