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The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces

Author

Listed:
  • Caicai Hu
  • Liang Guo
  • Francisco J. Garcia Pacheco

Abstract

Suppose that E,E′ are Q-regular Banach spaces, that G⊂E and G′⊂E′ are domains, and that f:G⟶G′ is a homeomorphism. The aim of this study is to prove that the quasisymmetric mapping under the quasihyperbolic metric is equivalent to the freely quasiconformal mapping under the condition E,E′ being Q-regular Banach spaces. This result is a partial solution to an open problem raised by Väisälä.

Suggested Citation

  • Caicai Hu & Liang Guo & Francisco J. Garcia Pacheco, 2022. "The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, December.
    • Handle: RePEc:hin:jjmath:5938029
    DOI: 10.1155/2022/5938029
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