The parameter conditions for the existence of the Hilbert-type multiple integral inequality and its best constant factor

被引：9

作者：

Hong, Yong ^{[1
]}

Huang, Qiliang ^{[2
]}

Chen, Qiang ^{[3
]}

机构：

[1] Guangdong Baiyun Univ, Dept Math, Guangzhou 510450, Guangdong, Peoples R China

[2] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China

[3] Guangdong Univ Educ, Dept Comp Sci, Guangzhou 510303, Guangdong, Peoples R China

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2021年 / 12卷 / 01期

关键词：

Hilbert-type multiple integral inequality; Homogeneous kernel; Parameter condition; Bounded operator; Operator norm; 26D10; 26D15;

D O I：

10.1007/s43034-020-00087-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By means of the weight function, the following results are given. The Hilbert-type multiple integral inequality with the lambda -order homogeneous kernel integral R+n</mml:msubsup>integral R+m</mml:msubsup>K(<mml:mfenced close="<parallel>" open="parallel to">x</mml:mfenced>m,rho,<mml:mfenced close="<parallel>" open="parallel to">y</mml:mfenced>n,rho )f(x)g(y)dxdy <= M<mml:msub><mml:mfenced close="<parallel>" open="parallel to">f</mml:mfenced>p,alpha <mml:msub><mml:mfenced close="<parallel>" open="parallel to">g</mml:mfenced>q,beta is true if and only if <mml:mfrac>alpha +mp</mml:mfrac>+<mml:mfrac>beta +nq</mml:mfrac>=lambda +m+n, and the expression of the best possible constant factor is obtained. Furthermore, its application in the operator theory is discussed.

引用

页数：15

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