New sphericalization and flattening mappings on metric spaces preserve doubling measures and Besov energies, with compositions biLipschitz equivalent to the original.
and Shanmugalingam, N., Conformal transformation of uniform domains under weights that depend on distance to the boundary, Anal
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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.