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arXiv · 2302.11094

Locally biH\"{o}lder continuous mappings and their induced embeddings between Besov spaces

Manzi Huang·Xiantao Wang·Zhuang Wang·Zhihao Xu
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Abstract

In this paper, we introduce a class of homeomorphisms between metric spaces, which are locally biH\"{o}lder continuous mappings. Then an embedding result between Besov spaces induced by locally biH\"{o}lder continuous mappings between Ahlfors regular spaces is established, which extends the corresponding result of Bj\"{o}rn-Bj\"{o}rn-Gill-Shanmugalingam (J. Reine Angew. Math. 725: 63-114, 2017). Furthermore, an example is constructed to show that our embedding result is more general. We also introduce a geometric condition, named as uniform boundedness, to characterize when a quasisymmetric mapping between uniformly perfect spaces is locally biH\"{o}lder continuous.

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Manzi Huang, Xiantao Wang, Zhuang Wang, Zhihao Xu. 2023-02-22. Locally biH\"{o}lder continuous mappings and their induced embeddings between Besov spaces. https://arxiv.org/abs/2302.11094

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