摘要
通过引入参数λ(1-q/p<λ≤2,p≥q>1)及两个非负且在(0,+∞)递增的可微函数u(x)和v(x)建立了一种广义带权的Hardy-Hilbert积分不等式.特别,当p=2时,得到经典Hilbert积分不等式的各种推广.作为应用,当u(x)和v(x)是幂函数、指数函数和对数函数时,建立了若干重要不等式.
It is shown that a Generalized Hardy-Hilbert integral inequality with weights can be established by introducing a parameter A （1 - q/p 〈λ≤ 2） and two nonnegative and increasing functions u （x） and v （x） which are differentiable in interval （0, ＋ ∞）. In particular, for case p = 2, the various new extensions of the classical Hilbert＇s integral inequality are obtained. As applications, some important inequalities are built, when u （x） and v （x） are power functions, exponent function and logarithm function.
出处
《纯粹数学与应用数学》
CSCD
北大核心
2008年第1期125-132,共8页
Pure and Applied Mathematics
基金
湖南省教育厅资助科研项目(06C657)
