若干新的p进制Hardy-Littlewood-Pólya型不等式

金建军

数学学报 ›› 2020, Vol. 63 ›› Issue (6) : 639-646.

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PDF(406 KB)
数学学报 ›› 2020, Vol. 63 ›› Issue (6) : 639-646. DOI: 10.12386/A2020sxxb0054
论文

若干新的p进制Hardy-Littlewood-Pólya型不等式

    金建军
作者信息 +

Some New p-adic Hardy-Littlewood-Pólya-type Inequalities

    Jian Jun JIN
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文章历史 +

摘要

本文建立了若干新的具最佳常数因子的p进制Hardy-Littlewood-Pólya型不等式,同时也给出了它们的等价形式以及一些特殊结果.

Abstract

In this note, we establish some new p-adic Hardy-Littlewood-Pólya-type inequalities with the best constant factors. The equivalent forms of these inequalities and some particular cases are also considered.

关键词

p进制域 / p进制积分算子 / p进制Hardy-Littlewood-Pó / lya型不等式 / 算子范数

Key words

p-adic field / p-adic integral operator / p-adic Hardy-Littlewood-Pólyatype inequalities / norm of operator

引用本文

导出引用
金建军. 若干新的p进制Hardy-Littlewood-Pólya型不等式. 数学学报, 2020, 63(6): 639-646 https://doi.org/10.12386/A2020sxxb0054
Jian Jun JIN. Some New p-adic Hardy-Littlewood-Pólya-type Inequalities. Acta Mathematica Sinica, Chinese Series, 2020, 63(6): 639-646 https://doi.org/10.12386/A2020sxxb0054

参考文献

[1] Fu Z. W., Wu Q. Y., Lu S. Z., Sharp estimates of p-adic Hardy and Hardy-Littlewood-Pólya operators, Acta Mathematica Sinica, English Series, 2013, 29(1):137-150.
[2] Hardy G. H., Littlewood J. E., Pólya G., Inequalities, Cambridge University Press, Cambridge, 1952.
[3] Kuang J. C., Applied Inequalities (in Chinese), Shandong Science and Technology Press, Ji'nan, 2004.
[4] Taibleson M. H., Fourier Analysis on Local Fields, Princeton University Press, Princeton, 1975.
[5] Vladimirov V. S., Volovich I. V., Zelenov E. I., p-Adic Analysis and Mathematical Physics, World Scientific, Singapore, 1994.

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