经典Hilbert不等式的p进制版本

doi:10.13371/j.cnki.chin.q.j.m.2020.04.012

数学季刊 ›› 2020, Vol. 35 ›› Issue (4): 431-440.doi: 10.13371/j.cnki.chin.q.j.m.2020.04.012

• • 上一篇

经典Hilbert不等式的p进制版本

1. School of Mathematics Sciences, Hefei University of Technology, Xuancheng Campus, Xuancheng 242000, China; 2. School of Computer Science and Information Engineering, Hefei University of Technology, Hefei 230009, China

收稿日期:2020-07-25 出版日期:2020-12-30 发布日期:2021-01-06
作者简介: JIN Jian-jun(1980-), male, native of Ezhou, Hubei, lecturer of Hefei University of Technology, engages in mathematical analysis and applications; LI Chun-hua(1983-), male, native of Shouxian, Anhui, associate professor of Hefei University of Technology, engages in electronic information science and technology.
基金资助:
Supported by National Science Foundation of China (Grant No. 11501157, 11705043, 11547137).

A Non-Archimedean Version of the Classical Hilbert Inequality

1. School of Mathematics Sciences, Hefei University of Technology, Xuancheng Campus, Xuancheng 242000, China; 2. School of Computer Science and Information Engineering, Hefei University of Technology, Hefei 230009, China

Received:2020-07-25 Online:2020-12-30 Published:2021-01-06
About author: JIN Jian-jun(1980-), male, native of Ezhou, Hubei, lecturer of Hefei University of Technology, engages in mathematical analysis and applications; LI Chun-hua(1983-), male, native of Shouxian, Anhui, associate professor of Hefei University of Technology, engages in electronic information science and technology.
Supported by:
Supported by National Science Foundation of China (Grant No. 11501157, 11705043, 11547137).

摘要/Abstract

摘要： In this note, we introduce and study a p-adic Hilbert-type integral operator and obtain its sharp norm estimate. As applications, we establish a p-adic Hilbert-type inequality with the best constant and its equivalent form.

关键词: p-Adic fields, p-Adic integral operator, p-Adic Hilbert-type inequality, Norm of operator

Abstract: In this note, we introduce and study a p-adic Hilbert-type integral operator and obtain its sharp norm estimate. As applications, we establish a p-adic Hilbert-type inequality with the best constant and its equivalent form.

Key words: p-Adic fields, p-Adic integral operator, p-Adic Hilbert-type inequality, Norm of operator

中图分类号:

O178

金建军, 李春华. 经典Hilbert不等式的p进制版本[J]. 数学季刊, 2020, 35(4): 431-440.

JIN Jian-jun, LI Chun-hua. A Non-Archimedean Version of the Classical Hilbert Inequality[J]. Chinese Quarterly Journal of Mathematics, 2020, 35(4): 431-440.

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经典Hilbert不等式的p进制版本

A Non-Archimedean Version of the Classical Hilbert Inequality

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