论Hilbert型积分不等式及其算子表示

On Hilbert-type Integral Inequalities and their Operator Expressions

引入独立参量,应用权函数的方法及实分析技巧,建立齐次与非齐次核两类Hilbert型积分不等式的等价联系,定义了等价的Hilbert型积分算子,还考虑了一些特殊核的范数.

By introducing independent parameters, applying the way of weight functions and using technique of real analysis, an equivalent connection of two kinds of Hilbert-type integral inequalities with the homogeneous kernels and the non-homogeneous kernels is provided. Furthermore, we define equivalent Hilbert-type integral operators and obtain the norms of some operators in particular kernels.