关于子区间逆向的Hilbert型积分不等式

A REVERSE HILBERT-TYPE INTEGRAL INEQUALITY ON A SUBINTERVAL

本文研究了建立逆向Hilbert型不等式问题.引入两对共轭指数,应用权函数,实分析及参量化的方法,在积分子区间上建立逆向的具有最佳常数因子及一般齐次核的Hilbert型积分不等式,等价式及一些特殊核的不等式,推广了一些文献的结果.

In this paper,we study the reverse Hilbert-type inequalities.By introducing two pairs of conjugate exponents and using the method of weight function and real analysis and the method of introducing parameters,a reverse Hilbert-type integral inequality and its equivalent forms on a subinterval with the best constant factors and the general homogeneous kernel are established and then some extensions of the published results are given.A few inequalities with particular kernels are considered.The theorems and lemmas provide and extend an amount of this type of inequalities.