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 non-empty 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.

Keywords

• Lipschitz-free space
• finite-dimensional Banach space
• divergence