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A New Hilbert-Type Inequality with the Homogeneous Kernel of Degree - 2 and with the Integral

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Abstract:

By using the weight functions and by means of Hadamard's inequality, we present a new Hilbert-type inequality with the integral in whole plane, a best constant factor and a homogeneous kernel of degree-2.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 7)
Pages:
9-17
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.7.9
Citation:
Z. Zheng et al., "A New Hilbert-Type Inequality with the Homogeneous Kernel of Degree - 2 and with the Integral", Bulletin of Mathematical Sciences and Applications, Vol. 7, pp. 9-17, 2014
Online since:
Feb 2014
Authors:
Zeng Zheng, Raja Rama Gandhi, Zi Tian Xie
Keywords:
Equivalent Form, Holder's Inequality, Single Parameter, Weight Function
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

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

Hardy G. H., Note on a theorem of Hilbert concerning series of positive terems, Proceedings London Math. Soc, 1925, 23(2): Records of Proc. XLV-XLVI.

Zitian Xie, A Hilbert-type integral inequality with the kernel of irrational expression, Mathematics in practice and theory, 2008, 38（16）：128-133.

Zitian Xie and Zeng Zheng , A Hilbert-type integral inequality whose kernel Is a homogeneous form of degree -3. Math. Anal. Appl., 2008, 339; 324-331.

Bicheng Yang, A new Hilbert-type integral inequality with some parameters, Journal of Jilin University(Science Edition), 2008, 46(6) : 1085-1090.

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

Xie Zitian, Zeng Zheng, A New Hilbert-Type integral inequality with the Homogeneous Kernel of Degree -2 and with the Integral in Whole Plane, Journal of Applied Mathematics and Bioinformatics, 2012, 2(1), 29-39.

Zheng Zeng and Zitian Xie, On a new Hilbert-type integral inequality with the the integral in whole 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 Benlu Fu, 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.

Xie Zitian, Zeng Zheng, A new half-discrete Hilbert-type inequality with the homogeneous kernel of degree -4, Journal of Jishou University(Naturnal Science Edition), 2012, 33 （2）15-19.

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.

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)，693-697.

Xie Zitian,K. Raja Rama Gandhi, Zeng Zheng, A new Hilbert-type integral inequality with the homogeneous kernel of real degree form and the integral in whole plane, Bulletin of Society for Mathematical Services & Applications, Vo2. No. 1, 2013, 95-109.

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