Calderón-Zygmund operators on lipschitz spaces over RD spaces

Abstract

Suppose that (X; d; ) is a metric measure space of homogeneous type in the sense of Coifman and Weiss with a reverse doubling condition. By establishing the Littlewood-Paley characterization of Lipschitz spaces, a density argument in the weak sense and almost orthogonality estimate we prove that a Calderon-Zygmund operator T is bounded on Lipschitz space if and only if T1 = 0.

Key words: Calderon-Zygmund operators, spaces of homogeneous type, RD spaces, Lip-schitz spaces.