乘积空间上的一类平均算子的L~p有界性(英文) |
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作者姓名: | 陈广洲 魏明权 燕敦验 |
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作者单位: | 中国科学院大学数学科学学院, 北京 100049 |
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基金项目: | Supported by the National Nature Science Foundation of China (11471039, 11271162) |
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摘 要: | 主要研究乘积空间上的一类算子Hφf(x)=∫10…∫10f(x1t1,…,xntn)φ(t1,…,tn)d t1…d tn在Lp上有界的充分必要条件,这个条件完全依赖于定义在0,1]×…×0,1]上的非负函数.此外,还给出了Hφ的算子范数.
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关 键 词: | 哈代算子 乘积空间 Lp" target="_blank">Lp')">Lp |
收稿时间: | 2014-12-24 |
修稿时间: | 2015-01-09 |
Lp-Bounds of a class of mean operators on product spaces |
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Authors: | CHEN Guangzhou WEI Mingquan YAN Dunyan |
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Institution: | College of Mathematica Science, University of Chinese Academy of Sciences, Beijing 100049 |
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Abstract: | We characterize a sufficient and necessary condition which ensures that the operator
Hφf(x)=...f(x1 t1,…,xn tnφ(t1,…,tn)dt1…dtn
is bounded on Lp(Gn) with 1≤p≤∞. The condition deeply depends on the nonnegative function φ defined on 0,1]×…×0,1]. Furthermore, the corresponding operator norms are worked out. |
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Keywords: | Hardy operator product space Lp" target="_blank">Lp')">Lp |
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