拟齐次核的半离散Hilbert型不等式的最佳搭配参数

The Best Matching Parameters for Semi-discrete Hilbert-type Inequality with Quasi-homogeneous Kernel

设G(u,v)是λ阶齐次函数,本文针对拟齐次核K(n,x)=G(n~(λ1),x~(λ1))(λ_1λ_2>0)的半离散Hilbert型不等式,利用权函数方法,讨论如何选取最佳搭配参数来获得具有最佳常数因子的不等式,得到最佳搭配参数的充分必要条件.最后讨论其在算子理论中的应用.

Suppose G(u,v)is a homogeneous function ofλorder,for the semi-discrete Hilbert-type inequality with quasi-homogeneous kernel K(n,x)=G(nλ1,xλ2)(λ1λ2>0).By using weight function method,how to choose the best matching parameters to obtain an inequality with the best constant factor is discussed,necessary and sufficient conditions for the best matching parameters are obtained.Finally,their applications to operator theory are discussed.