Chinese Quarterly Journal of Mathematics ›› 2020, Vol. 35 ›› Issue (4): 431-440.doi: 10.13371/j.cnki.chin.q.j.m.2020.04.012

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A Non-Archimedean Version of the Classical Hilbert Inequality

  

  1. 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).

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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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