中文摘要：

给出了一般Carnot群上的L^p加权Hardy型不等式,1＜p＜＋∞,由此导出了Hardy-Sobolev型不等式。作为对该不等式的一个应用，考虑了一类带异位势的p-sub-Laplace方程，对其弱解建立了二重性和唯一延拓性。

英文摘要：

We show L~p weighted Hardy type inequalities for 1 p ＋∞ on general Carnot groups.Using the previous inequalities,we also obtain a Hardy-Sobolev type inequality.As an application,doubling property and unique continuation of the weak solution to p-sub-Laplacian with singular weights are established.