| 崔尚斌.Heisenberg群上一类左不变LPDO的局部基本解及局部可解性[J].数学研究及应用,1989,9(2):257~266 |
| Heisenberg群上一类左不变LPDO的局部基本解及局部可解性 |
| Local Fundamental Solutions of a Class of Left Invariant Differential Operators on the Heisenberg Group |
| 投稿时间：1987-10-13 |
| DOI：10.3770/j.issn:1000-341X.1989.02.018 |
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| In this paper it is proved that local fundamental solution exists in some space Wm(Hn) (m∈Z), if the left invariant differential operator on the Heisenberg group Hn satisfies certain condition. The main results are:l.Let L be a left invariant differential operator on Hn. If there exist R≥0, r,s∈R and operators {Bλ|λ∈ΓR} ∈Vs(ΓR, Mr) such that, for almost all λ∈ΓR, Bλ is the right inverse of Ⅱλ(L), then there exists E∈Wm(Hn) (when m≥0 or m even) or E∈Wm-1(Hn) (when m<0 and odd) such that LE =δ(near the origie) Where m=min([r],-[2s]-n-2); 2. Let L(W,T) be of the form (3.1). If there exist R≥0 and r,s∈R such that when |λ|≥R,(?) and Cλ≥ C|λ|x(C>0), then the same conclusion as above holds with m=min(-[2r]-n-2,[-2s]-n-2). |
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