Some properties of quasisymmetries in metric spaces

Resumo

Let (X, d, μ) and (Y, d′, μ′) be metric spaces α-regular by Ahlfors with α > 0 and locally finite Borel measures μ and μ′, respectively. We consider the class ACS_E of absolutely continuous functions on a.a. compact subsets E ⊂ X and establish the membership of mappings f: X → Y to a given class.