Carnot群上的Hardy型不等式和唯一延拓性

Hardy Type Inequality and Unique Continuation on Carnot Groups

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,考虑了一类带奇异位势的p-sub-Laplace方程,对其弱解建立了二重性和唯一延拓性.

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.