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)
Author NameAffiliation
HONY Yong Department of Applied Mathematics, Guangzhou Huashang College,Guangzhou 511300, China. 
CHEN Qiang College of Computer Science, Guangdong University of Education, Guangzhou 510303, China. 
LI Zhen College of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China. 
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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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