论全平面Hilbert型积分不等式及其算子刻画

On a Hilbert-Type Integral Inequality in the Whole Plane and Operator Expression

引入独立参量,应用权函数的方法及实分析技巧,建立一个具有最佳常数因子的全平面非齐次核Hilbert型积分不等式,考虑了其等价式、逆式及相关的齐次式与Hardy型不等式;定义了全平面Hilbert型积分算子,还求出了一些特殊核的算子范数.

By introducing independent parameters, applying the way of weight functions and the technique of real analysis, a Hilbert-type integral inequality in the whole plane with a best possible constant factor and a non-homogeneous kernel is provided. The equivalent forms, the reverses, the related homogeneous homes and Hardy-type inequalities are considered. A Hilbert-type integral operator in the whole plane is defined, and the norms of operators for some particular kernels are obtained.