一个新积分核下的Hilbert型不等式及最佳常数因子

On a Hilbert-Type Inequality with a New Kernel and Its Best Constant Factor

引入独立参数,通过权系数方法,讨论新积分核K(x,y)=xμyμmax{xλ,yλ}下的一类Hilbert型不等式及其等价式,并通过参数μ和λ的适当选取,得到若干新的积分不等式.

A Hilbert-type Inequality with a new integral kernel K（x,y）=xμyμ/max{xλ,yλ}and its equivalent forms are studied, and some new integral inequalities are obtained by taking some parti- cular values of the parameters.