论文标题
Hausdorff操作员紧凑型Abelian团体
Hausdorff Operators on Compact Abelian Groups
论文作者
论文摘要
对于hausdorff操作员在广义强化空间上的界限$ h^p_e（g）$，真正的hardy空间$ h^1 _ {\ mathbb {r}}（g）$，$ bmo（g）$和$ bmoa（g）$ bmoa（g）$ g $ g $。令人惊讶的是，这些条件对于正在考虑的所有群体和空间都相同。给出了Dirichlet系列的应用程序。还考虑了$ g $上连续功能的空间和示例。
Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on $G$ and examples are also considered.
