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

Gonzalo Flores

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

Functional Analysis 2017-03-14 v1

Authors: Gonzalo Flores

Abstract

In this short note, we develop a method for identifying the spaces $Lip_{0}(U)$ 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 $L^{1}(U;\mathbb{R}^{n})$ .

Keywords

Lipschitz-free spaces identification open convex subsets quotient space Lip0 spaces

Cite

@article{arxiv.1703.04405,
  title  = {On an identification of the Lipschitz-free spaces over subsets of $\mathbb{R}^{n}$},
  author = {Gonzalo Flores},
  journal= {arXiv preprint arXiv:1703.04405},
  year   = {2017}
}

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