New sphericalization and flattening mappings on metric spaces preserve doubling measures and Besov energies, with compositions biLipschitz equivalent to the original.
and Zhou, Y., Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces, Forum Math
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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.