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arXiv · 1610.03966

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

Marek Cúth·Ondřej F. K. Kalenda·Petr Kaplický
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Abstract

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

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Marek Cúth, Ondřej F. K. Kalenda, Petr Kaplický. 2017-04-11. Isometric representation of Lipschitz-free spaces over convex domains in finite-dimensional spaces. https://doi.org/10.1112/s0025579317000031

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