A characterization of spaces of homogeneous type induced by continuous ellipsoid covers of Rn

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:505

Article

Bownik, Marcin¹  Li, Baode²  Weissblat, Tal³ 

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

[2] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[3] Hebrew Univ Jerusalem, Einstein Inst Math, IL-9190401 Givat Ram, Israel

关键词: Space of homogeneous type;    Quasi-convex;    Quasi-distance;    Continuous ellipsoid cover;   

DOI  :  10.1016/j.jmaa.2021.125482

来源: Elsevier

【 摘 要 】

We study the relationship between the concept of a continuous ellipsoid Theta cover of R-n, which was introduced by Dahmen, Dekel, and Petrushev [7,8,11], and the space of homogeneous type induced by Theta. We characterize the class of quasi-distances on R-n (up to equivalence) which correspond to continuous ellipsoid covers. This places firmly continuous ellipsoid covers as a subclass of spaces of homogeneous type on R-n satisfying quasi-convexity and 1-Ahlfors-regularity. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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