带参数的Hardy-Hilbert型不等式的精化

Refinement of Hardy-Hilbert Type Inequalities with Parameters

利用加强的Hlder不等式对Hardy-Hilbert型不等式做了改进,建立了一些新的形如∑∞n=0∑∞m=0ambn(2m+1)λ+(2n+1)λ<2λsin(ππ/p){∑m∞=0(2m+1)p-1-λapm}1p{∑n∞=0(2n+1)q-1-λbnq}1q(1-R)k的不等式.

An improvement of Haidy-Hilbert＇ s inequality can be obtained by means of a sharpening of Hoelder＇ s inequality, a newinequality of the form ∞∑n=0∞∑m=0ambn/（2m＋1）^λ〈π/2λsin（π/p）{∞∑m=0（2m＋1）^p-1-λam^p}1/p∞∑n=0（2n＋1）^q-1-λbn^q}1/q（1-R）^kis built.