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 APM  Vol.1 No.3 , May 2011
A Hilbert-Type Inequality with Some Parameters and the Integral in Whole Plane
Abstract: In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.
Cite this paper: nullZ. Xie and Z. Zeng, "A Hilbert-Type Inequality with Some Parameters and the Integral in Whole Plane," Advances in Pure Mathematics, Vol. 1 No. 3, 2011, pp. 84-89. doi: 10.4236/apm.2011.13019.
References

[1]   G. H. Hardy, J. E. Littlewood and G. Polya, “Inequalities,” Cambridge University Press, Cambridge, 1952.

[2]   G. H. Hardy, “Note on a Theorem of Hilbert Concerning Series of Positive Terems,” Proceedings of London Mathematical Soci-ety, Vol. 23, No. 2, 1925, pp. 45-46.

[3]   B. C. Yang, “A New Hilbert-Type Integral Inequality with a Parameters,” Journal of Henan University (Natural Science), Vol. 35, No. 4, 2005, pp. 4-8.

[4]   Z. T. Xie and Z. Zeng, “A Hilbert-Type Integral Inequality whose Kernel is a Homogeneous Form of De-gree-3,” Journal of Mathematical Analysis Application, Vol 339, No. 1, 2008, pp. 324-331 doi:10.1016/j.jmaa.2007.06.059

[5]   B. C. Yang, “A New Hilbert-Type Integral Inequality with Some Parameters,” Journal of Jilin University (Science Edition), Vol. 46, No. 6, 2008, pp. 1085-1090.

[6]   B. C. Yang, “A Hilbert-Type Inter-gral Inequality with the Homogeneous Kernel of Real Num-ber-Degree,” Journal of Jilin University (Science Edition), Vol. 47, No. 5, 2009, pp. 887-892.

[7]   Z. T. Xie and X. D. Liu, “A New Hilbert-Type Integral Inequality and its Reverse,” Journal of Henan University, (Science Edition), Vol. 39, No. 1, 2009, pp. 10-13.

[8]   Z. Zeng and Z. T. Xie, “On a New Hil-bert-Type Integral Inequality with the Integral in Whole Plane,” Journal of Inequalities and Applications, Article ID 256796, 2010.

[9]   Z. T. Xie, B. C. Yang and Z. Zeng, “A New Hil-bert- type Integral Inequality with the Homogeneous Kernel of Real Number-Degree,” Journal of Jilin University (Science Edition), Vol. 48, No. 6, 2010, pp. 941-945.

[10]   Z. T. Xie and Z. Zeng, “On Generality of Hilbert’s Inequality with Best Con-stant Factor,” Natural Science Journal of Xiangtan University, Vol. 32, No. 3, 2010, pp. 1-4.

[11]   Z. T. Xie and B. L. Fu, “A New Hilbert-Type Integral Inequality with a Best Constant Factor,” Journal of Wuhan University (Natural Science Edi-tion), Vol. 55, No. 6, 2009, pp. 637-640.

[12]   Z. T. Xie and Z. Zeng, “The Hilbert-Type Integral Inequality with the System Kernel of Degree Homogeneous Form,” Kyungpook Mathematical Journal, Vol. 50, 2010, pp. 297-306.

[13]   Z. T. Xie and F. M. Zhou, “A Generalization of a Hilbert-Type Ine-quality with the Best Constant Factor,” Journal of Sichuan Normal University (Natural Science), Vol. 32, No. 5, 2009, pp. 626-629.

[14]   Z. T. Xie and Z. Zeng, “A Hilbert-Type Integral Inequality with a Non-Homogeneous Form and a Best Constant Factor,” Advances and Applications in Mathematical Sciens, Vol. 3, No. 1, 2010, pp. 61-71.

[15]   Z. Zeng and Z. T. Xie, “A New Hilbert-Type Integral Inequality with a Best Constant Factor,” Journal of South China Normal University (Natural Science Edition), Vol. 3, 2010, pp. 31-33.

 
 
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