Lipschitz spaces over non-porous sets

Key Points

• The Lipschitz spaces $ ext{Lip}_0(M)$ and $ ext{Lip}_0( ext{R}^n)$ are shown to be linearly isomorphic.
• Results hold for non-porous sets with positive $n$-dimensional Lebesgue measure.
• The findings extend to Carnot groups when equipped with a Carnot-Carathéodory metric.
• This work contributes to the understanding of functional analysis in non-porous geometric contexts.

Abstract