Two kinds of Hilbert-type integral inequalities in the whole plane

Journal of inequalities and applications

Bicheng Yang¹ 

关键词: Hilbert-type integral inequality;    weight function;    equivalent form;    reverse;    operator expression;    26D15;   

DOI  :  10.1186/s13660-014-0545-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

By the way of using real analysis and estimating the weight functions, two kinds of Hilbert-type integral inequalities in the whole plane with a non-homogeneous kernel and a homogeneous kernel are given. The constant factor related to the triangle functions is proved to be the best possible. We also consider the equivalent forms, the reverses, some particular cases, and two kinds of operator expressions.

【 授权许可】

CC BY