高维乘积空间上分数次Hardy算子的最佳界

doi:10.7523/j.issn.2095-6134.2020.01.001

中国科学院大学学报 ›› 2020, Vol. 37 ›› Issue (1): 1-5.DOI: 10.7523/j.issn.2095-6134.2020.01.001

• 数学与物理学 • 下一篇

高维乘积空间上分数次Hardy算子的最佳界

李翔¹, 魏明权², 燕敦验¹

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

收稿日期:2019-01-15 修回日期:2019-02-26 发布日期:2020-01-15
通讯作者: 魏明权
基金资助:
Supported by the National Nature Science Foundation of China (11471039), Project of Henan Provincial Department of Education (18A110028), and the Nanhu Scholar Program for Young Scholars of Xinyang Normal University

Sharp bounds for fractional Hardy operator on higher-dimensional product spaces

LI Xiang¹, WEI Mingquan², YAN Dunyan¹

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

Received:2019-01-15 Revised:2019-02-26 Published:2020-01-15
Supported by:
Supported by the National Nature Science Foundation of China (11471039), Project of Henan Provincial Department of Education (18A110028), and the Nanhu Scholar Program for Young Scholars of Xinyang Normal University

摘要/Abstract

摘要： 得到高维乘积空间上分数次Hardy算子从L¹（R^n₁×…×R^n_m）到wL^Q（R^n₁×…×R^n_m）的最佳界。更一般地，还得到高维乘积空间上分数次Hardy算子从L^P（R^n₁×…×R^n_m）到L^Q_I（R^n₁×…×R^n_m）的算子范数。

关键词: 分数次哈代算子, 算子范数, 乘积空间, L^Q_I

Abstract: In this paper, we get the sharp bounds for fractional Hardy operator on higherdimensional product spaces from L¹(R^n₁×…×R^n_m) to the space wL^Q(R^n₁×…×R^n_m). More generally, the norm of fractional Hardy operator on higher-dimensional product spaces from L^P(R^n₁×…×R^n_m) to L^Q_I(R^n₁×…×R^n_m) is obtained.

Key words: fractional Hardy operator, operator norm, product space, L^Q_I

中图分类号:

O177

李翔, 魏明权, 燕敦验. 高维乘积空间上分数次Hardy算子的最佳界[J]. 中国科学院大学学报, 2020, 37(1): 1-5.

LI Xiang, WEI Mingquan, YAN Dunyan. Sharp bounds for fractional Hardy operator on higher-dimensional product spaces[J]. , 2020, 37(1): 1-5.

[1]	魏明权, 燕敦验. 乘积空间上的广义哈代算子的有界性[J]. 中国科学院大学学报, 2016, 33(4): 433-437.
[2]	陈广洲, 魏明权, 燕敦验. 乘积空间上的一类平均算子的L^p有界性[J]. 中国科学院大学学报, 2015, 32(4): 437-440.
[3]	刘琼. 两个新的积分不等式和一个算子范数关系式[J]. 中国科学院大学学报, 2015, 32(3): 398-403.

高维乘积空间上分数次Hardy算子的最佳界

Sharp bounds for fractional Hardy operator on higher-dimensional product spaces

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