应用数学2025，Vol.38Issue(2)：424-434,11.
超齐次核最优半离散高维Hilbert型不等式的等价条件及应用
Equivalence Conditions of Optimal Half-discrete High-dimensional Hilbert-type Inequalities with Super-homogeneous Kernel and Applications
摘要
Abstract
Introducing the super-homogeneous kernel and high-dimensional vector mode,by using the weight function method and real analysis techniques,the half-discrete Hilbert-type inequalities with super-homogeneous kernel in the high-dimensional weighted Lebesgue space and Hilbert-type space are discussed,equivalence conditions for the best matching parameters and the formula for the optimal con-stant factor are obtained.finally,the results obtained are used to discuss the boundedness and norm of operator with supper-homogeneous kernel.关键词
超齐次核/半离散高维Hilbert型不等式/最佳搭配参数/最佳常数因子/有界算子/算子范数Key words
Super-homogeneous kernel/Half-discrete high-dimensional Hilbert-type inequality/The best matching parameter/The best constant factor/Bounded operator/Operator norm分类
数理科学引用本文复制引用
洪勇..超齐次核最优半离散高维Hilbert型不等式的等价条件及应用[J].应用数学,2025,38(2):424-434,11.基金项目
广州华商学院特色科研项目(2024HSTS08) （2024HSTS08）
广东省基础与应用基础研究基金(2022A1515012429) （2022A1515012429）
