高维乘积空间上反向分数次Hardy不等式的最佳常数

doi:10.6040/j.issn.1671-9352.0.2023.331

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (8): 20-27.doi: 10.6040/j.issn.1671-9352.0.2023.331

高维乘积空间上反向分数次Hardy不等式的最佳常数

刘小玉(),魏明权*(),宋鹏超

信阳师范大学数学与统计学院, 河南信阳 464000

收稿日期:2023-07-25 出版日期:2024-08-20 发布日期:2024-07-31
通讯作者: 魏明权 E-mail:liuxy465@163.com;weimingquan11@mails.ucas.ac.cn
作者简介:刘小玉(2000—), 女, 硕士研究生, 研究方向为调和分析及其应用. E-mail: liuxy465@163.com
基金资助:
信阳师范大学2024年研究生科研创新基金资金项目(2024KYJJ057);信阳师范大学“南湖学者奖励计划”青年项目

Sharp constant for reverse fractional Hardy inequality on higher-dimensional product spaces

Xiaoyu LIU(),Mingquan WEI*(),Pengchao SONG

School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan, China

Received:2023-07-25 Online:2024-08-20 Published:2024-07-31
Contact: Mingquan WEI E-mail:liuxy465@163.com;weimingquan11@mails.ucas.ac.cn

摘要/Abstract

摘要：

研究了高维乘积空间上反向分数次Hardy不等式在加幂权Lebesgue空间中成立的条件, 并给出了该不等式的最佳常数。

关键词: 分数次Hardy算子, 旋转方法, 反向Hölder不等式, 反向Minkowski不等式, 最佳常数

Abstract:

The conditions for the validity of the reverse fractional Hardy inequality in power-weighted Lebesgue spaces are studied, and the sharp constant for the inequality is given.

Key words: fractional Hardy operator, rotation method, reverse Hölder's inequality, reverse Minkowski's inequality, sharp constant

中图分类号:

O174.2

刘小玉,魏明权,宋鹏超. 高维乘积空间上反向分数次Hardy不等式的最佳常数[J]. 《山东大学学报(理学版)》, 2024, 59(8): 20-27.

Xiaoyu LIU,Mingquan WEI,Pengchao SONG. Sharp constant for reverse fractional Hardy inequality on higher-dimensional product spaces[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(8): 20-27.

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高维乘积空间上反向分数次Hardy不等式的最佳常数

Sharp constant for reverse fractional Hardy inequality on higher-dimensional product spaces

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