与广义B-G向量场相关的Campanato空间的Morrey定理

Morrey's theorem of Campanato spaces related to generalized Baouendi-Grushin vector fields

通过证明广义Baouendi-Grushin向量场诱导的拟球满足A性质,证明了与该向量场相关的Campanato空间的Morrey定理.并利用Morrey定理,证明了当1<p≤Q(Q为与向量场相关的齐次维数)时,与广义Baouendi-Grushin向量场相关的Sobolev嵌入定理也是成立的.

By proving the balls induced by generalized Baouendi-Grushin vector fields satisfy A-property,the Morrey′s theorem of Campanato spaces associated with these vector fields is obtained.With this result,a Sobolev′s embedding theorem when 1〈p≤Q,where Q is the homogenous dimension related to these vector fields is checked.