Isomorphisms between spaces of Lipschitz functions
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Data
2019
Autores
Candido, Leandro 
Tipo
Artigo
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Resumo
We develop tools for proving isomorphisms of normed spaces
of Lipschitz functions over various doubling metric spaces and Banach
spaces. In particular, we show that Lip0(Zd) ≃ Lip0(Rd), for all d ∈ N.
More generally, we e.g. show that Lip0(Γ) ≃ Lip0(G), where Γ is from
a large class of finitely generated nilpotent groups and G is its Mal’cev
closure; or that Lip0(ℓp) ≃ Lip0(Lp), for all 1 ≤ p < ∞.
We leave a large area for further possible research.