论文标题
Triebel-lizorkin和besov空间的最佳嵌入式嵌入式空间
Optimal Embeddings for Triebel-Lizorkin and Besov Spaces on Quasi-Metric Measure Spaces
论文作者
论文摘要
在本文中，通过对所考虑的措施的某些下限条件，作者完全表征了sobolev嵌入的hajłasz-Triebel-lizorkin和Hajłasz-Besov空间在准量表衡量标准的一般背景下的sobolev嵌入，用于平滑度参数$ s $ s $。这项工作的一个有趣的方面是，这些嵌入的上述特征的范围是如何与基础空间的几何构成密切相关的（以定量方式）。此外，尽管在准中空间的背景下为Hajłasz-Triebel-Lizorkin和Hajłasz-Besov空间表示，本文的主要结果甚至改善了已知的工作，即使是公制设置中的Sobolev空间。
In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Hajłasz-Triebel-Lizorkin and Hajłasz-Besov spaces in the general context of quasi-metric measure spaces for an optimal range of the smoothness parameter $s$. An interesting facet of this work is how the range of $s$ for which the above characterizations of these embeddings hold true is intimately linked (in a quantitative manner) to the geometric makeup of the underlying space. Moreover, although stated for Hajłasz-Triebel-Lizorkin and Hajłasz-Besov spaces in the context of quasi-metric spaces, the main results in this article improve known work even for Sobolev spaces in the metric setting.
