Locally biH\"{o}lder continuous mappings and their induced embeddings between Besov spaces
Functional Analysis
2023-02-23 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2302.11094,
title = {Locally biH\"{o}lder continuous mappings and their induced embeddings between Besov spaces},
author = {Manzi Huang and Xiantao Wang and Zhuang Wang and Zhihao Xu},
journal= {arXiv preprint arXiv:2302.11094},
year = {2023}
}