Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12119 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $M$ be a subset of $\mathbb{R}^n$. If $M$ is not porous, in particular if it has positive $n$-dimensional Lebesgue measure, we prove that the Lipschitz spaces $\mathrm{Lip}_0(M)$ and $\mathrm{Lip}_0(\mathbb{R}^n)$ are linearly isomorphic. The result also holds more generally if $\mathbb{R}^n$ is replaced with a Carnot group equipped with its Carnot-Carathéodory metric.