SUBELLIPTIC ESTIMATES AND FUNCTION SPACES ON NILPOTENT LIE GROUPS
SUBELLIPTIC ESTIMATES AND FUNCTION SPACES ON NILPOTENT LIE GROUPS
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DOI：
10.1007/bf02386204
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发表时间：
1975-01-01
影响因子：
0.7
通讯作者：
FOLLAND, GB
中科院分区：
文献类型：
--
作者：
FOLLAND, GB
In recent years there has been considerable activity in the study of hypoelliptic but non-elliptic partial differential equations.(We recall that a differential operator~ e on a manifold M is said to be hypoelliptic if for any open set Uc M and distributions f, g on U satisfying 5ef= g on U, fCcg'(U) implies gEOg-(U).) One of the major ideas in this field is that of obtaining control over the characteristic directions of a differential operator by conditions involving commutators of vector fields or pseudodifferential operators. The prototype of such results is the following theorem of H6rmander [10]:(0.1) Proposition. Let Xo, X1...., X, be real vector fields on an open set UcR N, and let~ be the linear span of the vector fields Xi~,[Xh, Xi2],...,[[..,[Xi,, Xj,....... Xi~ _l], Xj (O<-ij<= n, l~ j<-k). Suppose there is an integer m such that~ spans the tangent space at every point of U. Then the operator. o~= X o+ z~ X~ is hypoelliptic on U.
