拟齐次核的Hilbert型级数不等式的最佳搭配参数条件及应用

The Best Matching Parameters Conditions of Hilbert-Type Series Inequality with Quasi-Homogeneous Kernel and Applications

选择搭配参数a,b,利用权函数方法可得Hilbert型级数不等式∞∑n=1∞∑m=1K(m,n)a_(m)b_(n)≤M(a,b)‖a‖_(p,α(a,b))‖b‖_(q,β(a,b)).该文讨论a,b应如何选取才能使具有拟齐次核的不等式中M(a,b)为最佳常数因子的问题,得到了a,b为最佳搭配参数的充分必要条件及最佳常数因子的表达式.最后讨论其在求算子范数中的应用.

Choosing a,b as the matching parameters,we can sue the weight function method to obtain Hilbert-type series inequality ∞∑n=1∞∑m=1K(m,n)a_(m)b_(n)≤M(a,b)‖a‖_(p,α(a,b))‖b‖_(q,β(a,b)).in the paper,the problem of how to choose a,b in order to make M(a,b) the best constant factor in inequality with quasi-homogeneous kernels are discussed,necessary and sufficient conditions are obtained for a,b to the best matching parameters,the formula for the best constant factor is obtained.Finally,their applications to solving operator morn are discussed.