Isomorphisms between spaces of Lipschitz functions

Abstract

We prove that normed linear spaces of Lipschitz functions defined on R^d and Z^d are linearly isomorphic. Moreover, our method of proof is aplicable in more general situations and so we obtain also results for various "doubling" metric spaces (e.g.

Carnot groups and their subsets) and for various infinite-dimensional Banach spaces.

Keywords

• Lipschitz functions
• Carnot groups
• Lipschitz-free spaces
• Orlicz spaces