Rellich type inequalities related to Grushin type operator and Greiner type operator  

作　　者：SHEN Shou-feng JIN Yong-yang 

机构地区：[1]Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310032,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2012年第3期353-362,共10页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation(NSF) of China (11001240);NSF of Zhejiang Province(Y6090359)

摘　　要：We prove some sharp Hardy inequality associated with the gradient △γ=（△x,｜x｜γ [x△y） by a direct and simple approach. Moreover, similar method is applied to ob- tain some weighted sharp Rellich inequality related to the Grushin operator in the setting of L^p. We also get some weighted Hardy and Rellich type inequalities related to a class of Greiner type operators.We prove some sharp Hardy inequality associated with the gradient △γ=（△x,｜x｜γ [x△y） by a direct and simple approach. Moreover, similar method is applied to ob- tain some weighted sharp Rellich inequality related to the Grushin operator in the setting of L^p. We also get some weighted Hardy and Rellich type inequalities related to a class of Greiner type operators.

关 键 词：Rellich inequality Hardy inequality Grushin type operator Greiner type operator. 

分 类 号：O178[理学—数学] TQ172.613[理学—基础数学]