数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 968-977.

• 论文 • 上一篇    下一篇

齐次核诱导的p进制积分算子及其应用

金建军1,*(),唐树安2(),冯小高3()   

  1. 1 合肥工业大学宣城校区基础部 安徽宣城 242000
    2 贵州师范大学数学科学学院 贵阳 550001
    3 西华师范大学数学与信息学院 四川南充 637009
  • 收稿日期:2020-07-17 出版日期:2021-08-26 发布日期:2021-08-09
  • 通讯作者: 金建军 E-mail:jinjjhb@163.com;tsa@gznu.edu.cn;fengxiaogao603@163.com
  • 作者简介:唐树安, E-mail: tsa@gznu.edu.cn|冯小高, E-mail: fengxiaogao603@163.com
  • 基金资助:
    国家自然科学基金(11501157);国家自然科学基金(12061022);国家自然科学基金(11701459)

On a $p$-Adic Integral Operator Induced by a Homogeneous Kernel and Its Applications

Jianjun Jin1,*(),Shuan Tang2(),Xiaogao Feng3()   

  1. 1 School of Mathematics Sciences, Hefei University of Technology, Xuancheng Campus, Anhui Xuancheng 242000
    2 School of Mathematics Sciences, Guizhou Normal University, Guiyang 550001
    3 College of Mathematics and Information, China West Normal University, Sichuan Nanchong 637009
  • Received:2020-07-17 Online:2021-08-26 Published:2021-08-09
  • Contact: Jianjun Jin E-mail:jinjjhb@163.com;tsa@gznu.edu.cn;fengxiaogao603@163.com
  • Supported by:
    the NSFC(11501157);the NSFC(12061022);the NSFC(11701459)

摘要:

该文引入并研究了一个核为$-λ$齐次的$p$进制积分算子,同时给出了该算子的精确范数估计.作为应用,建立了若干新的具有最佳常数因子的$p$进制不等式及其等价式,这些结果推广和丰富了已有文献中的相关结果.

关键词: p进制积分算子, p进制不等式, 齐次核, 算子范数

Abstract:

In this paper, we introduce and study a $p$-adic integral operator induced by a homogeneous kernel of degree $-λ$ and obtain its sharp norm estimates. As applications, we establish some new $p$-adic inequalities with the best constant factors and their equivalent forms, which extend some known results in the literature.

Key words: p-Adic integral operator, p-Adic inequalities, Homogeneous kernel, Norm of operator

中图分类号: 

  • O178