| 洪勇,李真,陈强.核为G(nλ1xλ2)(λ1λ2 > 0)的半离散Hilbert型不等式成立的等价参数条件及应用*[J].数学年刊A辑,2021,42(3):279~288 |
| 核为G(nλ1xλ2)(λ1λ2 > 0)的半离散Hilbert型不等式成立的等价参数条件及应用* |
| Equivalent Parameter Condition for the Establishment of Half-Discrete Hilbert-Type Inequality with Kernel G(nλ1xλ2)(λ1λ2 > 0) and Applications |
| Received:October 25, 2019 Revised:December 16, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0022 |
| 中文关键词: 非齐次核, 充要条件, 半离散Hilbert型不等式, 有界算子, 算子范数 |
| 英文关键词:Non-homogeneous kernel, The necessary and sufficient condition, HalfDiscrete Hilbert-type inequality, Bounded operator, Operator norm |
| 基金项目:国家自然科学基金(No.61772140) |
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| 中文摘要: |
| 利用权函数方法和实分析技巧, 在λ1λ2 > 0 的条件下,讨论具有非齐次核K(n,x)=G(nλ1xλ2)的半离散Hilbert型不等式成立的等价参数条件及最佳常数因子问题, 最后讨论其在算子理论中的应用. |
| 英文摘要: |
| By using the way of weight function and techniques of real analysis, in the case of λ1λ2 > 0, equivalent parameter condition for the establishment of half-discrete Hilbert-type inequality with kernel (nλ1xλ2) is given, the best possible constant factor is obtained, and theirs applications in operator theory are discussed. |
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