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arXiv · 2507.12119

Lipschitz spaces over non-porous sets

Ramón J. Aliaga
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Abstract

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-Carath\'eodory metric.

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Ramón J. Aliaga. 2025-07-16. Lipschitz spaces over non-porous sets. https://doi.org/10.1016/j.jfa.2026.111439

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