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 rela...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.展开更多
基金Supported by the National Natural Science Foundation(NSF) of China (11001240)NSF of Zhejiang Province(Y6090359)
文摘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.
