A reverse quasiconformal composition problem for Qα(Rn)

Jie Xiao Memorial University Yuan Zhou Beihang University

Analysis of PDEs mathscidoc:1912.43047

Arkiv for Matematik, 57, (2), 451-469
We give a partial converse to [8, Theorem 1.3] (as a resolution of [2, Problem 8.4] for the quasiconformal Q-composition) for Q0<α<2−1(Rn≥2), and yet demonstrate that if f:R2→R2 is a homeomorphism then the boundedness of u↦u∘f on Q2−1<α<1(R2)⊂BMO(R2) yields the quasiconformality of f.
quasi-conformality, composition, Essén–Janson–Peng–Xiao’s space, reverse
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@inproceedings{jiea,
  title={A reverse quasiconformal composition problem for Qα(Rn)},
  author={Jie Xiao, and Yuan Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204142606273521603},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={2},
  pages={451-469},
}
Jie Xiao, and Yuan Zhou. A reverse quasiconformal composition problem for Qα(Rn). Vol. 57. In Arkiv for Matematik. pp.451-469. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204142606273521603.
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