作 者: ;
机构地区: 广东教育学院
出 处: 《数学杂志》 1999年第4期421-425,共5页
摘 要: 本文建立如下权函数的不等式w (x) = ∫∞01x + y + 1(x + 1y + 1)1/2dy ≤π[1 - 1 - 2/π(x + 1)1/2] (x ∈[0,∞)),这里,常数1- 2/π是最佳值,从而改进了积分型Hilbert定理,作为应用,建立一个Hilbert类积分不等式及其加强式;并改进推广了Hardy-Littew ood 积分不等式. In this paper, we prove the inequality of the weight function w(x) as followsw(x)=∫ ∞ 01x+y+1(x+1y+1) 1/2 dy≤π[1-1-2/π(x+1) 1/2 ] (x∈[0,∞)),where the constant 1-2/ π is the best value. Then, an improvement of the integral type Hilbert theorem is given. As applications, we build a Hilbert type integral inequality and its strengthened version, and Hardy Littlewood integral inequality is refined and generalized.