We study the relationship between the concept of a continuous ellipsoid Θ cover of ${\mathbb{R}}^n$, which was introduced by Dahmen, Dekel, and Petrushev [7], [8], [11], and the space of homogeneous type induced by Θ. We characterize the class of quasi-distances on ${\mathbb{R}}^n$ (up to equivalence) which correspond to continuous ellipsoid covers. This places firmly continuous ellipsoid covers as a subclass of spaces of homogeneous type on ${\mathbb{R}}^n$ satisfying quasi-convexity and 1-Ahlfors-regularity.

中文翻译：

---

由连续椭球覆盖引起的齐次型空间的刻画 ${\mathbb{电阻}}^n$

我们研究了一个连续椭球 Θ 覆盖的概念之间的关系 ${\mathbb{电阻}}^n$由 Dahmen、Dekel 和 Petrushev [7]、[8]、[11] 引入，以及由 Θ 诱导的齐次型空间。我们刻画了类上的准距离${\mathbb{电阻}}^n$（直到等价）对应于连续椭球覆盖。这将牢固连续的椭球体覆盖作为均匀类型空间的子类放置在${\mathbb{电阻}}^n$ 满足拟凸性和 1-Ahlfors-正则性。