摘要
以Hilbert不等式为代表的双线型不等式是分析学的重要不等式.近代,由于改进了权系数方法及引入独立参量,使该类不等式的推广应用研究得到深入发展.本文通过引入单参数及估算权系数,建立一个具有最佳常数因子的-2齐次核的双线型不等式及其等价式,并考虑了逆向不等式及一些特殊参量的情形.
The bilinear inequalities including Hilbert＇s inequality are important in analysis and its applications. In recent years,by improving the way of weight coefficient and introducing the independent parameters,some research on the extensions and applications of this type of inequalities are developed. In this paper, by obtaining the weight coefficient, a bilinear inequality with the kernel of -2- order homogeneous and the best constant factor is given. The equivalent form,the reverse inequality and some particular cases are considered.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2006年第6期752-755,共4页
Journal of Xiamen University：Natural Science
基金
广东高校自然科学基金(0177)
广东教育学院教授博士专项经费资助
关键词
双线型不等式
权系数
核
等价式
Hilbert-type inequality
weight coefficient
kernel
equivalent form
