| 王爱珍,杨必成.一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式[J].数学年刊A辑,2024,(1):25~38 |
| 一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式 |
| A New Half-Discrete Hilbert-Type Inequality Involving One Multiple Upper Limit Function and One Partial Sums |
| Received:March 27, 2023 Revised:December 30, 2023 |
| DOI：10.16205/j.cnki.cama.2024.0003 |
| 中文关键词: 权函数, Euler-Maclaurin求和公式, Abel部分求和公式, 半离散Hilbert型不等式, 多重可变上限函数, 部分和 |
| 英文关键词:Weight function Euler-Maclaurin summation formula Abel's summation by parts formula Half-Discrete Hilbert-type inequality Multiple variable upper limit function Partial sums |
| 基金项目:国家自然科学基金(No.61772140)； 2020年度广东省普通高校特色创新项目(No.2020KTSCX088) |
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| 中文摘要: |
| 应用权函数的方法,Euler-Maclaurin求和公式,Abel部分求和公式及实分析技巧,求出了一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式.作为应用,考虑了特殊参数下不等式中最佳常数因子联系多参数的等价条件及一些特殊不等式. |
| 英文摘要: |
| By means of the weight functions, Euler-Maclaurin summation formula, Abel's summation by parts formula, and the technique of real analysis, a new half-discrete Hilbert-type inequality involving one multiple variable upper limit function and one partial sums is given. As applications, the equivalent conditions of the best possible constant factor in a particular inequality related to a few parameters and several particular inequalities are considered. |
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