一个半离散零齐次核的Hilbert型不等式

A Half-Discrete Hilbert-Type Inequality with the Homogeneous Kernel of Degree 0

以Hilbert不等式为代表的双线型不等式是分析学的重要不等式.近代,由于改进了权系数方法及引入独立参量,使该类不等式的推广应用研究得到深入发展.通过引入参数及估算权系数,给出一个新的具有最佳常数因子的半离散零齐次核为arctan（x/n）~λ（λ〉0）的Hilbert型不等式,同时给出了相应的等价形式.

The bilinear inequalities including Hilbert＇ s inequality are important in analysis and its applications. In recent years, by improving the way of weight coefficient and introducing the independent parameters, some research on the extensions and applications of this type of inequalities are developed. In this paper, by introducing some parameters and estimating the weight function, a new half-discrete Hilbert-type inequality with the Homogeneous Kernel of Degree 0 as arctan（x/n）λ（λ/0） and a best constant factor is given. The equivalent forms are considered.