【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.更多还原

【Abstract】 It is shown that a Generalized Hardy-Hilbert integral inequality with weights can be established by introducing a parameterλ(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.更多还原