| 带幂权Morrey空间上Hausdorff算子的最佳界 |
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| 作者姓名： | 张兴松 魏明权 燕敦验 |
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| 作者单位： | 1. 中国科学院大学数学科学学院, 北京 100049;2. 信阳师范学院数学与统计学院, 河南信阳 464000 |
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| 基金项目： | Supported by the National Nature Science Foundation of China (11871452), Project of Henan Provincial Department of Education (18A110028), and the Nanhu Scholar Program for Young Scholars of Xinyang Normal University |
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| 摘 要： | 分别得到定义在带幂权Morrey空间Lp，λ（$\mathbb{R}^n$，|x|αdx）和带幂权齐次中心Morrey空间$\dot B$p，λ（$\mathbb{R}^n$，|x|αdx）上的Hausdorff算子$\mathscr{H}_Φ$的范数.并把这些结果推广到乘积Hausdorff算子$\mathscr{H}$Φm.
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| 关 键 词： | Hausdorff算子 乘积Hausdorff算子 Morrey空间 |
| 收稿时间： | 2019-12-23 |
| 修稿时间： | 2020-03-02 |
Sharp bound of Hausdorff operators on Morrey spaces with power weights |
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| Authors: | ZHANG Xingsong WEI Mingquan YAN Dunyan |
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| Institution: | 1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;2. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan, China |
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| Abstract: | In this paper, we calculate the norm of the Hausdorff operator $\mathscr{H}_Φ$ defined on the Morrey space with power weights Lp,λ($\mathbb{R}^n$,|x|αdx) and the homogeneous central Morrey space with power weights $\dot B$p,λ($\mathbb{R}^n$,|x|αdx), respectively. We also extend our results to the product Hausdorff operator $\mathscr{H}$Φm. |
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| Keywords: | Hausdorff operator product Hausdorff operator Morrey space |
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