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.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 7)

Pages:

9-17

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:

February 2014

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, 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.

Cited By:

[1] Z. Zeng, X. Zitian, "A New Multiple Hilbert-Type Integral Inequality With A Non-Homogeneous Form", i-manager’s Journal on Mathematics, Vol. 4, p. 25, 2015

DOI: https://doi.org/10.26634/jmat.4.3.3597[2] B. Yang, S. Wu, Q. Chen, "On an extended Hardy-Littlewood-Polya’s inequality", AIMS Mathematics, Vol. 5, p. 1550, 2020

DOI: https://doi.org/10.3934/math.2020106[3] B. Yang, S. Wu, Q. Chen, "A New Extension of Hardy-Hilbert’s Inequality Containing Kernel of Double Power Functions", Mathematics, Vol. 8, p. 894, 2020

DOI: https://doi.org/10.3390/math8060894