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.
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
Online 15 15

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.