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Erschienen in:
2017 | OriginalPaper | Buchkapitel
Microlocal Solvability and Subellipticity of Several Classes of Pseudodifferential Operators with Involutive Characteristics
verfasst von : P. R. Popivanov
Erschienen in: Generalized Functions and Fourier Analysis
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In this paper pseudodifferential operators with involutive characteristics are considered in two different cases: elliptic subprincipal symbol and subprincipal symbol being a symbol of principal type near some characteristic point (i.e., vanishing at a part of the characteristic set). We prove (micro)local non-solvability results as well as subelliptic estimates in the second case when the loss of regularity is of the following type: $$ \frac{{2k + 1}} {{k + 1}} = 1 + \frac{k} {{k + 1}},\,k \in {\Bbb N} $$ . For the operators of subprincipal type interesting results were proved recently by N. Dencker.