A New Hilbert-Type Inequality In Whole Plane With The Homogeneous Kernel Of Degree 0

Xie Zitian*, Zheng Zeng**
* Department of Mathematics, Zhaoqing University, Zhaoqing & Shaoguan University, Shaoguan, Guangdong, China.
** Shaoguan University, Shaoguan, Guangdong, China.
Periodicity:January - March'2013
DOI : https://doi.org/10.26634/jmat.2.1.2159

Abstract

In this paper, by estimating the weight function, we give a new Hilbert-type inequality in whole plane with the homogeneous kernel of degree 0 . As its applications, we consider the equivalent and a particular result.

Keywords

Hilbert-type integral inequality; weight function; Holder's inequality;equivalent form

How to Cite this Article?

Xie, Z., and Zeng, Z. (2013). A New Hilbert-Type Inequality In Whole Plane With The Homogeneous Kernel Of Degree 0. i-manager’s Journal on Mathematics, 2(1), 13-20. https://doi.org/10.26634/jmat.2.1.2159

References

[1]. Hardy G. H., Littlewood J. E. and Polya G., (1952). Inequalities, Cambridge University Press, Cambridge.
[2]. Bicheng Yang, (2006). On the the norm of an intergal operator and applications, J. Math. Anal. Appl, 321,182-192.
[3]. Zitian Xie and Zheng Zeng, (2010). A Hilbert-type Integral Inequality with a Non-homogeneous Form and a best constant factor, Advances and applications in mathmatical sciences, 3,(1),61-71
[4]. Zitian Xie and Zeng Zheng, (2008). A Hilbert-type integral inequality whose kernel is a homogeneous form of degree -3,J.Math.Appl, (339):324-331.
[5]. Xie Zitian, Zeng Zheng, (2010). On generality of Hilbert's inequality with best constant factor, Natural Science Journal of Xiangtan University, 32(3),1-4
[6]. Bicheng Yang, (2008). A Hilbert-type with a mixed kemel and extensions, Journal of Sichuan Normal University(Natural Science), 31(3):281-284.
[7]. Zitian Xie, Zheng Zeng, (2010). The Hilbert-type integral inequality with the system kernel of degree homogeneous form, Kyungpook Mathematical Journal (50),297-306
[8]. Zheng Zeng and Zitian Xie, (2010). On a new Hilbert-type integral inequality with the the integral in whole plane,, Journal of Inequalities and Applications, Vol., Article ID 256796, 8 pages, 2010. doi:10.1155/2010/256796
[9]. Zitian Xie, Bicheng Yang, Zheng Zeng, (2010). A New Hilbert-type integral inequality with the homogeneous kernel of real number-degree, Journal of Jilin University (Science Edition), 48(6)941-945.
[10]. Zitian Xie and Benlu Fu, (2009). A new Hilbert-type integral inequality with the best constant factor, J.Wuhan Univ. (Nat.Sci.Ed), 55(6):637-640.
[11]. Dongmei Xin, (2009). On a Hilbert-type integral inequality, Kyungpook Mathe.J., (49):393-401.
[12]. Zitian Xie and Xingdong Liu, (2009). A new Hilbert-type integral inequality and its reverse, Journal of Henan University (Science Edition), 39(1),10-13.
[13]. Xie Zitian, (2011). A New Hilbert-type integral inequality with the homogeneous kernel of real number-degre, Journal of Jishou University(Natural Science Edition),32(4),26-30
[14]. Zheng Zeng and Zitian Xie, (2010). A new Hilbert-type integral inequality with a best constant factor, Journal of South China Normal University (Natural Science Edition) (3), 31-33
[15]. Bicheng Yang, (2006). On the norm of an integral operatorand applications, J. Math. Anal. Appl, 321: 182-192.
[16]. Xie Zitian, Zeng Zheng, (2012). A new half-discrete Hilbert-type inequality with the homogeneous kernel of degree, Journal of Jishou University(Natural Science Edition), 33 (2), 15-19.
[17]. Zitian Xie, Zheng Zeng, Qinghua Zhou, (2012). A new Hilbert-type integral inequality with the homogeneous kernel of real number-degree and its equivalent inequality forms, Journal of Jilin University (Science Edition), 50(4), 693-697.
[18]. Jichang Kang, (2004). Applied Inequalities, Shangdong Science and Technology press, Jinan, 6.
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