论文标题
在Hausdorff操作员上，在本地紧凑型组的同质空间上
On Hausdorff operators on homogeneous spaces of locally compact groups
论文作者
论文摘要
Hausdorff运算符在实际线路和多维欧几里得空间上，源自某些经典的求和方法。现在是一个活跃的研究领域。自2019年以来，作者对一般组的Hausdorff运营商进行了定义和研究。本文的目的是在Lebesgue上定义和研究Hausdorff运营商，以及在本地紧凑型组的同质空间上定义和研究真正的Hardy空间。我们特别介绍了在本地紧凑型组的均匀空间上的一个原子硬质空间，并获得了Hausdorff操作员在此类空间上的界定条件。考虑了几种推论，并提出了未解决的问题。
Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated.
