The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces

Caicai Hu, Liang Guo and Francisco J. Garcia Pacheco

Journal of Mathematics, 2022, vol. 2022, 1-10

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5938029

DOI: 10.1155/2022/5938029

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