New sphericalization and flattening mappings on metric spaces preserve doubling measures and Besov energies, with compositions biLipschitz equivalent to the original.
and Kumagai, T., Heat kernel estimates for jump processes of mixed types on metric measure spaces, Probability Theory Related Fields 140 (2008), 277–317
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Preserving Besov (fractional Sobolev) energies under sphericalization and flattening
New sphericalization and flattening mappings on metric spaces preserve doubling measures and Besov energies, with compositions biLipschitz equivalent to the original.