论半离散的 Hilbert 型不等式及其算子表示

摘要

By introducing independent parameters,applying the way of weight functions and technique of real analysis,an equivalent connection of two kinds of half-discrete Hilbert-type inequalities with the homogeneous kernels and the non-homogeneous kernels are provided.Furthermore,we define equivalent half-discrete Hilbert-type operators and obtain the norms of operators in some particular kernels.%引入独立参量及中间变量，应用权函数方法及实分析技巧，建立齐次与非齐次核半离散Hilbert 型不等式的等价联系，定义了等价的半离散 Hilbert 型算子，还考虑了一些特殊核的范数表示。