高维乘积空间上分数次Hardy算子的最佳界

李翔; 魏明权; 燕敦验

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: https://doi.org/10.7523/j.issn.2095-6134.2020.01.001

数学与物理学

高维乘积空间上分数次Hardy算子的最佳界

李翔 ,
魏明权 ,
燕敦验

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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

网络出版日期: 2020-01-15

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

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

LI Xiang ,
WEI Mingquan ,
YAN Dunyan

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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 date: 2019-01-15

Revised date: 2019-02-26

Online published: 2020-01-15

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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

本文引用格式

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 . DOI: 10.7523/j.issn.2095-6134.2020.01.001

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

参考文献

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