一个有限区间的Hilbert型积分不等式

A Hilbert-type Integral Inequality on the Finite Interval

以Hilbert不等式为特例的Hilbert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应用了参量化思想,使该类不等式的研究得到深入发展.该文引入多参数,应用实分析的方法以估算权函数,在有限区间(a,b)(0<a<b<∞)建立若干类Hilbert型积分不等式及其等价式.作为应用,还考虑了一些特殊核的情形.

Hilbert-type 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 researches on the extensions and applications of this type of inequalities are further developed. In this paper, by introducing some parameters and using the way of analysis, the weight functions are estimated, and a few classes of Hilbert-type integral inequality and the equivalent form on the finite interval （a,b）（1〈a〈b〈∞） are given. As applications, a lot of cases of the particular kernel are considered.