论文标题
Sobolev，Triebel-lizorkin和Besov的嵌入和扩展域的量度表征
A Measure Characterization of Embedding and Extension Domains for Sobolev, Triebel-Lizorkin, and Besov Spaces on Spaces of Homogeneous Type
论文作者
论文摘要
在本文中，对于（定量）取决于基础空间的几何构成的平滑度参数$ s $的最佳范围，作者确定了纯粹测量的理论条件，这些条件完全表征了hajłasz-hajłasz--triebel-lizorkin Spaces $ m^s_ s_ p，p，q} $和q} $的嵌入和扩展域的表征$ n^s_ {p，q} $在均质类型的一般空间中。尽管在准中空间的背景下说明，这些特征即使在公制设置中也可以改善相关工作。特别是，作为本文的主要结果的必然学，作者在一般倍增度量度量空间的背景下为Sobolev嵌入和扩展域获得了新的特征。
In this article, for an optimal range of the smoothness parameter $s$ that depends (quantitatively) on the geometric makeup of the underlying space, the authors identify purely measure theoretic conditions that fully characterize embedding and extension domains for the scale of Hajłasz--Triebel--Lizorkin spaces $M^s_{p,q}$ and Hajłasz--Besov spaces $N^s_{p,q}$ in general spaces of homogeneous type. Although stated in the context of quasi-metric spaces, these characterizations improve related work even in the metric setting. In particular, as a corollary of the main results in this article, the authors obtain a new characterization for Sobolev embedding and extension domains in the context of general doubling metric measure spaces.
