Multidimensional Exponential Inequalities with Weights

Canadian mathematical bulletin

Dah-Chin Luor¹ 

[1] Department of Applied Mathematics, I-Shou University, Ta-Hsu, Kaohsiung 84008, Taiwan

关键词: multidimensional inequalities;    geometric mean operators;    exponential inequalities;    star-shaped regions;   

DOI  :  10.4153/CMB-2010-038-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We establish sufficient conditions on the weight functions $u$ and $v$ for the validity of the multidimensional weighted inequality $$ Bigl(int_E Phi(T_k f(x))^q u(x),dxBigr)^{1/q} le C Bigl (int_E Phi(f(x))^p v(x),dxBigr )^{1/p}, $$ where 0<$p$, $q$<$infty$, $Phi$ is a logarithmically convex function, and $T_k$ is an integral operator over star-shaped regions. The condition is also necessary for the exponential integral inequality. Moreover, the estimation of $C$ is given and we apply the obtained results to generalize some multidimensional Levin--Cochran-Lee type inequalities.

【 授权许可】

Unknown