Hardy-Hausdorff spaces on the Heisenberg group

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• 作者：Kai Zhao
• 关键词：Hardy ; Hausdorff space ; tent space ; Heisenberg group ; atomic decomposition ; predual
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：59
• 期：11
• 页码：2167-2184
• 全文大小：302 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862
• 卷排序：59

文摘

In this paper, by using the tent spaces on the Siegel upper half space, which are defined in terms of Choquet integrals with respect to Hausdorff capacity on the Heisenberg group, the Hardy-Hausdorff spaces on the Heisenberg group are introduced. Then, by applying the properties of the tent spaces on the Siegel upper half space and the Sobolev type spaces on the Heisenberg group, the atomic decomposition of the Hardy-Hausdorff spaces is obtained. Finally, we prove that the predual spaces of Q spaces on the Heisenberg group are the Hardy-Hausdorff spaces.