论文标题
BESOV和Triebel-Lizorkin空间在同质类型的空间上，并应用于Calderón-Zygmund操作员的界限
Besov and Triebel-Lizorkin Spaces on Spaces of Homogeneous Type with Applications to Boundedness of Calderón-Zygmund Operators
论文作者
论文摘要
在本文中，作者在Coifman和Weiss的意义上介绍了Besov和Triebel-lizorkin的空间，证明这些（IN）同质性Besov和Triebel-Lizorkin空间与Exp-atis（或Exp-iatis）（或exp-iatis）（或exp-iactians）以及基本属性的分布和一些基本属性的选择无关。作为应用，作者表明，某些已知功能空间与某些特殊情况的BESOV和Triebel-Lizorkin空间一致，此外，在这些BESOV和Triebel-Lizorkin空间上获得了Calderón-Zygmund运算符的界限。所有这些结果在很大程度上取决于通过其二元立方体反映的几何特性，其所考虑的均匀类型空间。将这些空间的已知理论在度量度量空间上进行比较，本文的主要新颖性是，本文中介绍的所有结果都摆脱了对基础空间的考虑量度的反向加倍假设的依赖，因此给出了这些功能空间对同质类型空间的最终空间理论。
In this article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (in)homogeneous Besov and Triebel-Lizorkin spaces are independent of the choices of both exp-ATIs (or exp-IATIs) and underlying spaces of distributions, and give some basic properties of these spaces. As applications, the authors show that some known function spaces coincide with certain special cases of Besov and Triebel-Lizorkin spaces and, moreover, obtain the boundedness of Calderón-Zygmund operators on these Besov and Triebel-Lizorkin spaces. All these results strongly depend on the geometrical properties, reflected via its dyadic cubes, of the considered space of homogeneous type. Comparing with the known theory of these spaces on metric measure spaces, a major novelty of this article is that all results presented in this article get rid of the dependence on the reverse doubling assumption of the considered measure of the underlying space and hence give a final real-variable theory of these function spaces on spaces of homogeneous type.
