An extended Hilbert’s integral inequality in the whole plane with parameters

Journal of Inequalities and Applications

Yin Li¹  Leping He¹  Bicheng Yang² 

[1] College of Mathematics and Statistics, Jishou University;Department of Mathematics, Guangdong University of Education;

关键词: Hilbert’s integral inequality;    Weight function;    Equivalent form;    Operator;    Norm;   

DOI  :  10.1186/s13660-018-1810-z

来源: DOAJ

【 摘 要 】

Abstract By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert’s integral inequality in the whole plane with parameters and a best possible constant factor is provided. The equivalent forms, the reverses, and the related homogeneous forms with particular parameters are considered. Meanwhile, an extended Hilbert’s integral operator in the whole plane is defined, and the operator expressions for the equivalent inequalities are obtained.

【 授权许可】

Unknown