Homeomorphisms of the Heisenberg group preserving BMO

Riikka Korte1, Niko Marola2, Olli Saari1
1Department of Mathematics and Systems Analysis, Aalto University, Aalto, Finland
2Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

Tóm tắt

We provide a new geometric proof of Reimann’s theorem characterizing quasiconformal mappings as the ones preserving functions of bounded mean oscillation. While our proof is new already in the Euclidean spaces, it is applicable in Heisenberg groups as well as in more general stratified nilpotent Carnot groups.

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Tài liệu tham khảo

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