JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 20-27.doi: 10.6040/j.issn.1671-9352.0.2023.331

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

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

  1. 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

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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

CLC Number: 

  • O174.2
1 HARDY G H .Note on a theorem of Hilbert[J].Mathematische Zeitschrift,1920,6(3/4):314-317.
2 FARIS W G .Weak Lebesgue spaces and quantum mechanical binding[J].Duke Mathematical Journal,1976,43(2):365-373.
3 CHRIST M , GRAFAKOS L .Best constants for two nonconvolution inequalities[J].Proceedings of the American Mathematical Society,1995,123(6):1687-1693.
doi: 10.1090/S0002-9939-1995-1239796-6
4 LU Shanzhen , YAN Dunyan , ZHAO Fayou .Sharp bounds for Hardy type operators on higher-dimensional product spaces[J].Journal of Inequalities and Applications,2013,2013(1):1-11.
doi: 10.1186/1029-242X-2013-1
5 ZHAO Fayou , LU Shanzhen .The best bound for n-dimensional fractional Hardy operators[J].Mathematical Inequalities & Applications,2015,18(1):233-240.
6 WANG Shimo , LU Shanzhen , YAN Dunyan .Explicit constants for Hardy's inequality with power weight on n-dimensional product spaces[J].Science China Mathematics,2012,55(12):2469-2480.
doi: 10.1007/s11425-012-4453-4
7 HE Qianjun , LI Xiang , YAN Dunyan .Sharp bounds for Hardy type operators on higher-dimensional product spaces[J].Frontiers of Mathematics in China,2018,13(6):1341-1353.
doi: 10.1007/s11464-018-0740-x
8 HUANG Zhenxiao , SHI Yanping , YANG Bicheng .On a reverse extended Hardy-Hilbert's inequality[J].Journal of Inequalities and Applications,2020,2020(68):1-14.
9 LIAO Jianquan , YANG Bicheng .A new reverse extended Hardy-Hilbert's inequality with two partial sums and parameters[J].Axioms,2023,12(7):1-13.
10 FAN Dashan , ZHAO Fayou .Sharp constants for multivariate Hausdorff q-inequalities[J].Journal of the Australian Mathematical Society,2019,106(2):274-286.
doi: 10.1017/S1446788718000113
11 HARDY G H , LITTLEWOOD J E , PÓLYA G .Inequalities[M].Cambridge: Cambridge University Press,1952.
12 FU Z W , GRAFAKOS L , LU S Z , et al.Sharp bounds for m-linear Hardy and Hilbert operators[J].Houston Journal of Mathematics,2012,38(1):225-244.
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