On a New Hilbert-Type Intergral Inequality with the Intergral in Whole Plane
1 Department of Mathematics, Shaoguan University, Shaoguan, Guangdong 512005, China
2 Department of Mathematics, Zhaoqing University, Zhaoqing, Guangdong 526061, China
Journal of Inequalities and Applications 2010, 2010:256796 doi:10.1155/2010/256796Published: 2 August 2010
By introducing some parameters and estimating the weight functions, we build a new Hilbert's inequality with the homogeneous kernel of 0 order and the integral in whole plane. The equivalent inequality and the reverse forms are considered. The best constant factor is calculated using Complex Analysis.