Zygmund graphs are thin for doubling measures

Abstract

The Zygmund functions form an intermediate class between Lipschitz and H\"older functions; their second order divided differences are uniformly bounded. It is well known that for $d \geq 1$ the graph of any Lipschitz function $f:\R^d \rightarrow \R$ is thin for doubling measures, and we extend this result to the Zygmund class.