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.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 3)

Pages:

71-82

Citation:

Z. T. Xie et al., "A New Hilbert-Type Integral Inequality with the Homogeneous Kernel of Real Degree Form and the Integral in Whole Plane", Bulletin of Mathematical Sciences and Applications, Vol. 3, pp. 71-82, 2013

Online since:

Feb 2013

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

Hardy G. H., Littlewood J. E. and Polya G., Inequalities, London, Cambridge University Press, Cambridge, (1952).

Hardy G. H., Note on a theorem of Hilbert concerning series of positive terms, Proceedings London Math. Soc., 1925, 23(2): 45-46.

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.

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.

Jianhua Xhong and Bicheng Yang, On a relation to four basic Hilbert-type integral inequalities, Applied Mathematical Sciences, Vol. 4, 2010, no, 19, 923-930.

XIE Zitian and ZHOU Qinghua, A note on a Property of psi -function, Wuhan University Journal of Natural Sciences, Wuhan University Journal of Natural Science, 2011, 16(2), 139-142.

Bicheng Yang, On a Hilber-type integral inequality with a combination kerne and applications, Kyungpook Mathematical Journal, 2010(50), 281-288.

Zitian Xie , Zheng Zeng, The Hilbert-type integral inequality with the system kernel of - λ degree homogeneous form, Kyungpook Mathematical Journal, 2010(50), 297-306.

Xie Zitian, A New Hilbert-type integral inequality with the homogeneous kernel of real numberdegre, Journal of Jishou University(Natural Science Edition), 2011, 32(4)26-30.

Zitian Xie and Bicheng Yang, A new Hilbert-type integral inequality with some parameters and its reverse, Kyungpook Mathematical Journal, 2008, (48): 93-100.

Zitian Xie, A new Hilbert-type inequality with the kernel of -3-homogeneous, Journal of Jilin University (Science edition), 2007, 45(3): 369-373.

Zitian Xie and Juming Murong, A rewerse Hilbert-type inequality with some parameters, Journal of Jilin University (Science edition), 2008, 46 (4): 665-669.

Zitian Xie, A new reverse Hilbert-type inequality with a best constant facter, J. Math. Appl, 2008, (343): 1154-1160.

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.

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.

Zheng Zeng and Zitian Xie, On a new Hilbert-type integral inequality with the integral in w- hole plane, Journal of Inequalities and Applications vol. 2010, Article ID 256796, 8 pages, 2010. doi: 10. 1155/2010/256796.

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.

Zitian Xie and Fang min Zhou, A generalization of a Hilbert-type inequality with the best constant factor, Journal of Sichuan Normal University (Natural Science) 2009, 32(5): 626-629.

Xie Zitian, Zeng Zheng, A Hilbert-type integral inequality with the integral in whole plane and the kernel of -4 degree homogeneous form, i-manager's Journal on Mathematics, Vol. 1 No. 3, Julyseptember 2012, 6-12.

Zitian Xie, Zheng Zeng, Qinghua Zhou , 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), 2012, 50(4)ɼ693-697.

Xie Zitian, Zeng Zheng, A new half-discrete Hilbert-type inequality with the homogeneous kernel of degree -4μ, Journal of Jishou University(Natural Science Edition), 2012, 33215-19.