Zygmund graphs are thin for doubling measures

The Zygmund functions form an intermediate class between Lipschitz and Holder functions; their second order divided differences are uniformly bounded. It is well known that for d >= 1 the graph of any Lipschitz function f : Rd -> R is thin for doubling measures, and we extend this result to the Zygmund class.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

Zygmund functions are a type of functions that fall between Lipschitz and Holder functions. Their second order divided differences are uniformly bounded. We extend the well-known result about Lipschitz functions to the Zygmund class.