| 洪勇,陈强,李真.拟齐次核的 Hilbert 型重积分不等式最佳搭配参数的等价条件及应用*[J].数学年刊A辑,2022,43(2):191~200 |
| 拟齐次核的 Hilbert 型重积分不等式最佳搭配参数的等价条件及应用* |
| Equivalence Conditions of the Optimal Matching Parameters for Hilbert-Type Multiple Integral Inequality with Quasi-homogeneous Kernel and Applications |
| Received:October 14, 2020 Revised:November 24, 2021 |
| DOI：10.16205/j.cnki.cama.2022.0012 |
| 中文关键词: 拟齐次核, Hilbert型重积分不等式, 最佳常数因子, 最佳搭配参数, 等价条件, 有界算子, 算子范数 |
| 英文关键词:Quasi-homogeneous kernel, Hilbert-type multiple integral inequality, The best constant factor, The optimal matching parameter,Equivalence condition, 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, 讨论拟齐次核Hilbert型重积分不等式的最佳搭配参数,得到最佳搭配参数的若干等价条件及不等式最佳常数因子的表达公式. 最后讨论其在奇异积分算子理论中的应用. |
| 英文摘要: |
| By using the weight function method, the optimal matching parameter conditions for Hilbert-type multiple integral inequality with quasi-homogeneous kernel are discussed,several equivalence conditions for optimal matching are obtained, and the formula for the expression of the best constant factor of the inequality is obtained. Finally, their applications to the theory of singular integral operator are discussed. |
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