On an identification of the Lipschitz-free spaces over subsets of ${\mathbb{R}}^n$

Abstract

In this short note, we develop a method for identifying the spaces $Li{p}_0(U)$ for every nonempty open convex $U$ of ${\mathbb{R}}^n$ and $n\in \mathbb{N}$. Moreover, we show that $\mathcal{F}(U)$ is identified with a quotient of $L^1(U;{\mathbb{R}}^n)$.