Isometric representation of Lipschitz-free spaces over convex domains in finite-dimensional spaces

Abstract

Let $E$ be a finite-dimensional normed space and $\Omega$ a nonempty convex open set in $E$. We show that the Lipschitz-free space of $\Omega$ is canonically isometric to the quotient of $L^1(\Omega ,E)$ by the subspace consisting of vector fields with zero divergence in the sense of distributions on $E$.

13 pages; few corrections were made and some references were added

References in corpus (2)

• On the structure of Lipschitz-free spaces
• The Metric Approximation Property and Lipschitz-Free Spaces over Subsets of ${\mathbb{R}}^N$

Cited by in corpus (5)

• Supports in Lipschitz-free spaces and applications to extremal structure
• On relations between transportation cost spaces and ${\ell }_1$
• Finitely additive measures and complementability of Lipschitz-free spaces
• Linear structure of functions with maximal Clarke subdifferential
• Tilings of the Hyperbolic Space and Lipschitz Functions