关于Hardy-Hilbert不等式的多参数推广

摘要

This paper carries out study on Hardy-Hilbert＇s inequality and makes the following improvement： provided that p1,1/p＋1/q=1,0A,B≤1,an,bn≥0,and 0∑∞n=0bqn∞,Then we have：∑∞m=0∑∞n=0ambn/Am＋Bn＋1{∑∞n=0（π/Bsin（π/p）-（3p-B）（p-1）/6p（2An＋）11/p）anp}1/p{∑∞n=0（π/Asin（π/p）-（3q-A）（q-1）/6q（2Bn＋1）1/q）bnq}1/q.The results presented in this paper improve and generalize some corresponding results in recent works.%对Hardy-Hilbert不等式进行了研究,并将其进一步改进如下：若p〉1,1/p＋1/q=1,0〈A,B≤1,an,bn≥0,使0〈∑∞n=0apn〈∞,0〈∑∞n=0bqn〈∞,则∑∞m=0∑∞n=0ambn/Am＋Bn＋1〈{∑∞n=0（π/Bsin（π/p）-（3p-B）（ p-1）/6p（2An＋）11/p）anp}1/p{∑∞n=0（π/Asin（π/p）-（3q-A）（q-1）/6q（2Bn＋1）1/q）bnq}1/q.所得结果改进和推广了最近文献的一些相应结果.