齐次核诱导的p进制积分算子及其应用

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

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 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 Jin^1,*(),Shuan Tang²(),Xiaogao Feng³()

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/Abstract

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

金建军,唐树安,冯小高. 齐次核诱导的p进制积分算子及其应用[J]. 数学物理学报, 2021, 41(4): 968-977.

Jianjun Jin,Shuan Tang,Xiaogao Feng. On a $p$-Adic Integral Operator Induced by a Homogeneous Kernel and Its Applications[J]. Acta mathematica scientia,Series A, 2021, 41(4): 968-977.

参考文献 7

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