Hilbert不等式的推广

Generalization of Hilbert inequality

利用变分方法对一般对称积分核情形的Hilbert不等式进行了推广,给出了此类型不等式系数的准确的上下界,对一种特殊情形,求出了不等式最佳系数的表达式.

Variational method is used to generalize Hilbert inequality for general symmetric kernel case. Exact upper and lower bound parameter of this type of inequality is obtained. For a special case, the formula of the parameter of the inequality is obtained.