English

Zygmund graphs are thin for doubling measures

Classical Analysis and ODEs 2023-06-23 v1 Functional Analysis

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 d1d \geq 1 the graph of any Lipschitz function f:RdRf:\R^d \rightarrow \R is thin for doubling measures, and we extend this result to the Zygmund class.

Keywords

Cite

@article{arxiv.2306.12852,
  title  = {Zygmund graphs are thin for doubling measures},
  author = {Claudio A. DiMarco},
  journal= {arXiv preprint arXiv:2306.12852},
  year   = {2023}
}
R2 v1 2026-06-28T11:11:51.981Z