Abstract
In this paper,we build a new Hilbert's inequality with the homogeneous kernel of real order and the integral in whole plane. The equivalent inequality is considered. The best constant factor is calculated using ψ function.
Highlights
E (1.1) T where the constant factor is the best possible
Inequality (1.1) is well-known as Hilbert's integral inequality,which has been extended by Hardy-Riesz as [2]: C we have the following Hardy-Hilbert's integral inequality: (1.2)
Hilbert's inequality attracts some attention in recent years.inequalities (1.1)and(1.2)
Summary
E (1.1) T where the constant factor is the best possible. Inequality (1.1) is well-known as Hilbert's integral inequality,which has been extended by Hardy-Riesz as [2]:C we have the following Hardy-Hilbert's integral inequality: (1.2)A where the constant factor is the best possible.Hilbert's inequality attracts some attention in recent years.inequalities (1.1)and(1.2)R have many generalizations and variations. (1.1) has been strengthened by Yang and others (including double series inequalities ). [3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21].In 2008, Zitian Xie and Zheng Zeng gave a new Hilbert-type Inequality [4] as follows T such that RE (1.3)where the constant factor is the best possible.In 2010,Jianhua Xhong and Bicheng Yang gave a new Hilbert-type Inequality [5] as follows : Assume that. Abstract: In this paper,we build a new Hilbert's inequality with the homogeneous kernel of real order and the integral in whole plane. The best constant factor is calculated using f unction. In 2008, Zitian Xie and Zheng Zeng gave a new Hilbert-type Inequality [4] as follows
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