中文摘要：

对构成广义Greiner算子的向量场Xj=δ/δxj＋2kyj｜z｜^2k-2δ/δt,Yj=δ/δyj-2kxj｜z｜^2k-2δ/δt,j=1,…,n,x,y,∈R^n,z=x＋√-1y,t∈R,k≥1,得到了拟球域内和拟球域外的Hardy型不等式；建立了广义Picone型恒等式，并由此导出比文献[3]更一般的全空间上的Hardy型不等式；并在P=2时建立了具最佳常数的Hardy型不等式．

英文摘要：

The vector fields Xj=δ/δxj＋2kyj｜z｜^2k-2δ/δt,Yj=δ/δyj-2kxj｜z｜^2k-2δ/δt,j=1,…,n,x,y,∈R^n,z=x＋√-1y,t∈R,k≥1,are considered. Hardy type inequalities in the pseudo ball and outside the pseudo ball are obtained. The generalized Picone type identity and then Hardy type inequalities on the whole space containing the known results in [3] are established. When p = 2 the sharp constant in the Hardy type inequality is discussed.