摘要
通过引入两个参数λ、s (s >1,(n - 1) (1- 1s <λ <n) ,将著名的Hilbert积分不等式推广到n (n 2 )重积分的情形 ,建立了不等式 ,系数Γn (λn) /Γ (λ)被证明是最好的 .特别 ,当n =2且λ =1时 。
In this paper,it is shown that the famous Hilbert integral inequality can be extended by introducing a weight funcition X n-λ-1 ,where the parameter λ satisifies constraint(n-1)(1-1s)<λ<n(with s>1 and n≥2,n∈N).The inequality of the form... r n + f 1(x 1)f 2(x 2)...f(x n)(x 1+x 2+...+x n)dx 1dx 2...dx nΓ n(λn)/Γ(λ)Πni=1 +∞ 0x n-2 f n i(x)dx 1nis established,and the coefficient Γ n(λn)/Γ(λ) is proved to be the best possible.In particular,when n=2 and λ=1,the classical Hilbert integral inequality is obtained.
出处
《韶关学院学报》
2002年第3期25-30,共6页
Journal of Shaoguan University
