A Non-Archimedean Version of the Classical Hilbert Inequality

JIN Jian-jun, LI Chun-hua

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

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 4: 431 - 440

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.04.012

A Non-Archimedean Version of the Classical Hilbert Inequality

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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

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.

Received date: 2020-07-25

Online published: 2021-01-06

Supported by

Supported by National Science Foundation of China (Grant No. 11501157, 11705043, 11547137).

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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

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

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