Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

BSMaSS > Volume 4 > A Hilbert-Type Integral Inequality with the...
A Hilbert-Type Integral Inequality with the Homogeneous Kernel of Degree-3 and a Best Constant Factor
< Back to Volume

A Hilbert-Type Integral Inequality with the Homogeneous Kernel of Degree-3 and a Best Constant Factor

Full Text PDF

Abstract:

By establishing the weight function, we present a new Hilbert-type inequality with the integral in whole plane and with a best constant factor, and its kernel is a homogeneous form of degree-3, and also we put forward its equivalent form.

Info:

Periodical:
The Bulletin of Society for Mathematical Services and Standards (Volume 4)
Pages:
41-46
DOI:
https://doi.org/10.18052/www.scipress.com/BSMaSS.4.41
Citation:
Z. T. Xie and Z. Zheng, "A Hilbert-Type Integral Inequality with the Homogeneous Kernel of Degree-3 and a Best Constant Factor", The Bulletin of Society for Mathematical Services and Standards, Vol. 4, pp. 41-46, 2012
Online since:
Dec 2012
Authors:
Zi Tian Xie, Zeng Zheng
Keywords:
Equivalent Form, Hilbert-Type Integral Inequality, Holder's Inequality, 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.

Bicheng Yang, A new Hilbert-type integral inequality with a parameters, Journal of Henan University(NaturalScience), 2005, 35(4)：4-8.

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.

Zitian Xie and Zheng Zeng, A Hilbert-type integral Iinequality with a non-homogeneous form and a best constant factor, Advances and applications in mathematical sciences, 2010, 3, (1), 61-71.

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, A new Hilbert-type integral inequality with the best constant factor, J. Wuhan Univ. (Nat. Sci. Ed) 2009, 55(6): 637-640.

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

Zitian Xie and Xingdong Liu, A new Hilbert-type integral inequality and its reverse, Journal of Henan University (Science Edition), 2009, 39(1)：10-13.

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, Liang Hongwei, A generalization of Hilbert-type inequality, Journal of Henan University (Natural Science), 2012，42（2），117-120.

Zitian Xie, A Hilbert-type integral inequality with a mix homogeneous kernel of real numberdegree, Journal of South China Normal University (Natural Science Edition), 2012, 44(3), 36-39.

Show More Hide