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Sphericalization and flattening in quasi-metric measure spaces

Qingshan Zhou,Xining Li,Saminathan Ponnusamy,Yaxiang Li

Journal of Mathematical Analysis and Applications（2022）

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Abstract
The purpose of the note is to explore the invariance properties of sphericalization and flattening in quasi-metric spaces. We show that the Ahlfors regular and doubling property of quasi-metric spaces are preserved under sphericalization and flattening transformations. As an application, we give an improvement of a recent result in [21].
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Key words
Quasi-metric spaces,Sphericalization,Flattening,Doubling condition,Ahlfors regular,Quasi-möbius
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