An Improvement of the Hardy-Hilbert Type Integral Inequalities and an Application

In this paper,it is shown that Hardy-Hilbert’s integral inequality with parameter is improved by means of a sharpening of Hlder’s inequality.A new inequality is established as follows: （integral fromαto∞）(integral fromαto∞)(f（x）g（y）/（x+y+2β）)dxdy <(π/sin（π/p）){（integral fromαto∞）f（x）dx}·{（integral fromαto∞）g（x）dx}·（1-R）, where R=(S（F,h）-S（G,h）),m=min{1/p,1/q}.As application;an extension of Hardy-Littlewood’s inequality is given.