A New Hilbert-type Integral Inequality with the Homogeneous Kernel of 1/2 Degree Form and the Integral in Whole Plane

Xie Zitian*, Zheng Zeng**
* Department of Math. Zhaoqing University, Zhaoqing, Guangdong, P. R. China.
** Shaoguan University, Shaoguan, Guangdong, China.
Periodicity:January - March'2012
DOI : https://doi.org/10.26634/jmat.1.1.1664

Abstract

In this paper, the authors build a new Hilbert's inequality with the homogeneous kernel of 1/2 order and the integral in whole plane. The equivalent inequality is considered. The best constant factor is calculated using Complex Analysis.

Keywords

Half-discrete, Hilbert-type integral inequality; H lder's inequality

How to Cite this Article?

Zitian, X., and Zheng, Z. (2012). A New Hilbert-Type Integral Inequality with The Homogeneous Kernel of ½ Degree Form and The Integral in Whole Plane. i-manager’s Journal on Mathematics, 1(1), 12-17. https://doi.org/10.26634/jmat.1.1.1664

References

[1]. Hardy G.H., Littlewood J.E., and P$\acute{o}$lya G., Inequalities, London, Cambridge University Press, Cambridge, 1952.
[2]. Hardy G.H., Note on a theorem of Hilbert concerning series of positive terms, Proceedings London Math. Soc., 1925,23(2):45-46.
[3]. Zitian Xie and Zheng Zeng, A Hilbert-type integral inequality whose kernel is a homogeneous form of degree -3, J.Math.Appl, 2008,(339):324-331.
[4]. Zitian Xie, Zheng Zeng, A Hilbert-type integral inequality with a non-homogeneous form and a best constant factor, Advances and Applications in Mathematical Sciens 2010,3(1), 61-71.
[5]. Zitian Xie , Zheng Zeng, The Hilbert-type integral inequality with the system kernel of degree homogeneous form, Kyungpook Mathematical Journal, 2010(50), 297-306.
[6]. Xie Zitian, A New Hilbert-type integral inequality with the homogeneous kernel of real number-degre, Journal of Jishou University(Natturnal Science Edition), 2011, 32(4), 26-30
[7]. Bicheng Yang, A new Hilbert-type integral inequality with some parameters, Journal of Jilin University (Science edition) 2008,46,(6): 1085-1090.
[8]. Zitian Xie and Bicheng Yang, A new Hilbert-type integral inequality with some parameters and its reverse, Kyungpook Mathematical Journal,2008,(48):93-100.
[9]. Zitian Xie and Juming Murong, A rewerse Hilbert-type inequality with some parameters, Journal of Jilin University (Science edition), 2008,46 (4):665-669.
[10]. Zitian Xie, A new reverse Hilbert-type inequality with a best constant facter, J.Math.Appl, 2008,(343):1154-1160.
[11]. Zheng Zeng and Zi-tian Xie, A Hilbert's inequality with a best constant factor, Journal of Inequalities and Applications, 2009, Article ID 820176, 8 pages doi:10.1155/2009/820176.
[12]. Xie Zitian ,Zeng Zheng, On generality of Hilbert's inequality with best constant factor, Natural Science Journal of Xiangtan University, 2010, 32(3): 1-4.
[13]. Zheng Zeng and Zitian Xie, On a new Hilbert-type integral inequality with the integral in whole plane, Journal of Inequalities and Applications ?vol. 2010, Article ID 256796, 8 pages, 2010. doi:10.1155/2010/256796.
[14]. Zitian Xie, Bicheng Yang, Zheng Zeng, A New Hilbert-type integral inequality with the homogeneous kernel of real number-degree, Journal of Jilin University(Science Edition), 2010, 48(6) : 941-945.
[15]. Xie Zitian, Zeng Zheng, A Hilbert-type integral inequality with the homogeneous kernel of real number-degree and its equivalent, Journal of Zhejiang University(Science Edition), 2011,38 (3),266-270.
[16]. Zitian Xie and Zheng Zeng, A Hilbert-type integral inequality with the integral in whole plane and its equivalent forms, Mathematica Aeterna, 2011,1 (8),577-586.
[17]. Xie Zitian, Zeng Zheng, On a Hilbert-type integral inequality with the homogeneous kernel of real number-degree and its operator form, Advances and Applications in Mathematical Sciences 2011,10(5),481-490
[18]. Xie Zitian, Zeng Zheng, A new Hilbert type integral inequality with the homogeneous kernel of degree 0, Journal of Southwest University(Natturnal Science Edition), 2011,23(8),137-141.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.