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

In the setting of a metric measure space (X, d, mu) with an n-dimensional Radon measure p, we give a necessary and sufficient condition for the boundedness of Calderon-Zygmund operators associated to the measure mu on Lipschitz spaces on the support of p. Also, for the Euclidean space R-d with an arbitrary Radon measure mu, we give several characterizations of Lipschitz spaces on the support of g, Lip(a, A), in terms of mean oscillations involving mu. This allows us to view the "regular" BMO space of X. Tolsa as a limit case for alpha -> 0 of the spaces Lip(a, mu).