一个全平面的Hilbert型积分不等式

A Hibert-type Integral Inequality on the Plane

通过应用权函数的方法及实分析的技巧,建立了全平面上一个新的具有最佳常数因子的-2齐次核为1/(x-y)2+axy(0<a<4)的Hilbert型积分不等式及其等价形式,并考虑了其逆向的情形.

By using the way of weight function and the technique of real analysis, a new Hihert - type Integral Ine-quality with -3 homogeneous kernel as1/（x-y）^2＋axy（0〈a〈4）and a best constant factor on the plane are giv-en. The equivalent form and the reverse forms are established.