A Hilbert-Type Integral Inequality in the Whole Plane with the Homogeneous Kernel of Degree −2

被引：0

作者：

Dongmei Xin

Bicheng Yang

机构：

[1] Guangdong Education Institute,Department of Mathematics

来源：

Journal of Inequalities and Applications | / 2011卷

关键词：

Weight Function; Constant Factor; Equivalent Form; Integral Formula; Integral Inequality;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

By applying the way of real and complex analysis and estimating the weight functions, we build a new Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree −2 involving some parameters and the best constant factor. We also consider its reverse. The equivalent forms and some particular cases are obtained.

引用

共 7 条

[1] Yang BC(2009)A survey of the study of Hilbert-type inequalities with parameters Advances in Mathematics 38 257-268
[2] Yang BC(2006)On the norm of an integral operator and applications Journal of Mathematical Analysis and Applications 321 182-192
[3] Xu J(2007)Hardy-Hilbert's inequalities with two parameters Advances in Mathematics 36 189-202
[4] Yang BC(2007)On the norm of a Hilbert's type linear operator and applications Journal of Mathematical Analysis and Applications 325 529-541
[5] Xin DM(2010)A Hilbert-type integral inequality with a homogeneous kernel of zero degree Mathematical Theory and Applications 30 70-74
[6] Yang BC(2010)A Hilbert-type integral inequality with a homogeneous kernel of degree zero Journal of Shandong University. Natural Science 45 103-106
[7] Yang BC(2006)A new Hilbert-type inequality Bulletin of the Belgian Mathematical Society 13 479-487

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