Hilbert不等式的加强及其应用

A Refinement of Hilbert's Inequality and Applications

通过引入一个形如x～(1/2)/1+x～(1/2)(x≥0)的函数,建立一种新的加权Hilbert不等式,并且给出权函数的具体表达式,从而得到经典Hilbert重级数定理的一个加强结果.作为它的应用,给出Hardy-Littlewood不等式和Widder不等式的一些改进.

This paper establishes a new refinement for Hilbert＇s inequality by means of the weight function method. As applications, improvement of the Hardy-Littlewood inequality and the Widder inequality are discussed.