december 2023 Locally biHölder continuous maps and their induced embeddings between Besov spaces
Manzi Huang, Xiantao Wang, Zhuang Wang, Zhihao Xu
Bull. Belg. Math. Soc. Simon Stevin 30(4): 468-481 (december 2023). DOI: 10.36045/j.bbms.230314

Abstract

We introduce a class of homeomorphisms between metric spaces, which are locally biHölder continuous maps. Then an embedding result between Besov spaces induced by locally biHölder continuous maps between Ahlfors regular spaces is established, which extends the corresponding result of Björn, Björn, Gill, and Shanmugalingam. 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 map between uniformly perfect spaces is locally biHölder continuous.

Citation

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Manzi Huang. Xiantao Wang. Zhuang Wang. Zhihao Xu. "Locally biHölder continuous maps and their induced embeddings between Besov spaces." Bull. Belg. Math. Soc. Simon Stevin 30 (4) 468 - 481, december 2023. https://doi.org/10.36045/j.bbms.230314

Information

Published: december 2023
First available in Project Euclid: 31 December 2023

Digital Object Identifier: 10.36045/j.bbms.230314

Subjects:
Primary: 30L10 , 46E36

Keywords: (power) quasisymmetric map , Ahlfors regular metric space , Besov space , ‎embedding‎ , Locally biHölder continuous map , uniform boundedness

Rights: Copyright © 2023 The Belgian Mathematical Society

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Vol.30 • No. 4 • december 2023
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