Equivalent Statements of Two Multidimensional Hilbert-Type Integral Inequalities with Parameters

被引：1
|
作者：
Li, Yiyuan [1 ]
Zhong, Yanru [2 ]
Yang, Bicheng [3 ]
机构：
[1] Guilin Univ Elect Technol, Sch Art & Design, Guilin 541004, Peoples R China
[2] Guilin Univ Elect Technol, Sch Comp Sci & Informat Secur, Guilin 541004, Peoples R China
[3] Guangdong Univ Educ, Sch Math, Guangzhou 510303, Peoples R China
来源：
AXIOMS | 2023年 / 12卷 / 10期
基金：
中国国家自然科学基金;
关键词：
transfer formula; multidimensional Hilbert-type inequality; gamma function; best possible constant factor;
D O I：
10.3390/axioms12100956
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as H(||x||alpha lambda 1||y||beta lambda 2) (lambda 1,lambda 2 not equal 0) are given, which are some extensions of the Hilbert-type integral inequalities in the two-dimensional case. Some equivalent conditions of the best value and several parameters related to the new inequalities are provided. Two corollaries regarding the kernel, represented as k lambda(||x||alpha lambda 1,||y||beta lambda 2)(lambda 1,lambda 2 not equal 0), are given, and a few new inequalities for the particular parameters are obtained.
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页数：13
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