Locally biHölder continuous maps and their induced embeddings between Besov spaces

被引：0

作者：

Huang, Manzi ^{[1
]}

Wang, Xiantao ^{[1
]}

Wang, Zhuang ^{[1
]}

Xu, Zhihao ^{[1
]}

机构：

[1] Hunan Normal Univ, Sch Math & Stat, MOE, LCSM, Changsha 410081, Hunan, Peoples R China

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2023年 / 30卷 / 04期

关键词：

Locally biHolder continuous map; (power) quasisymmetric map; Besov space; Ahlfors regular metric space; embedding; uniform boundedness; SOBOLEV SPACES;

D O I：

10.36045/j.bbms.230314

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a class of homeomorphisms between metric spaces, which are locally biHolder continuous maps. Then an embedding result between Besov spaces induced by locally biHolder continuous maps between Ahlfors regular spaces is established, which extends the corresponding result of Bjorn, Bjorn, 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 biHolder continuous.

引用

页码：468 / 481

页数：14

共 41 条

[31] Separating Maps between Spaces of Vector-Valued Absolutely Continuous Functions
Dubarbie, Luis
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2010, 53 (03): : 466 - 474
[32] A DE VRIES-TYPE DUALITY THEOREM FOR THE CATEGORY OF LOCALLY COMPACT SPACES AND CONTINUOUS MAPS. II
Dimov, G. D.
[J]. ACTA MATHEMATICA HUNGARICA, 2011, 130 (1-2) : 50 - 77
[33] A de Vries-type duality theorem for the category of locally compact spaces and continuous maps. II
G. D. Dimov
[J]. Acta Mathematica Hungarica, 2011, 130 : 50 - 77
[34] A de Vries-type duality theorem for the category of locally compact spaces and continuous maps. I
Dimov, G. D.
[J]. ACTA MATHEMATICA HUNGARICA, 2010, 129 (04) : 314 - 349
[35] A de Vries-type duality theorem for the category of locally compact spaces and continuous maps. I
G. D. Dimov
[J]. Acta Mathematica Hungarica, 2010, 129 : 314 - 349
[36] QUASI-ISOMETRIC AND WEAKLY QUASISYMMETRIC MAPS BETWEEN LOCALLY COMPACT NON-COMPLETE METRIC SPACES
Wang, Xiantao
Zhou, Qingshan
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 55 (03) : 967 - 970
[37] On Quasi Gyrolinear Maps between Mobius Gyrovector Spaces Induced from Finite Matrices
Watanabe, Keiichi
[J]. SYMMETRY-BASEL, 2021, 13 (01): : 1 - 10
[38] HYERS-ULAM STABILITY OF ISOMETRIES AND NON-EXPANSIVE MAPS BETWEEN SPACES OF CONTINUOUS FUNCTIONS
Vestfrid, Igor A.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (06) : 2481 - 2494
[39] Induced map on K -theory for certain T-equivariant maps between Hilbert spaces
Kato, Tsuyoshi
[J]. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2021, 15 (04) : 1433 - 1467
[40] Extension of quasi-Ho¨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{\text {o}}$$\end{document}lder embeddings between unit spheres of p-normed spaces
Rui Liu
Jifu Yin
[J]. Annals of Functional Analysis, 2023, 14 (2)

← 1 2 3 4 5 →