On the microlocal hypoellipticity of pseudodifferential operators (Q761629)

This paper deals with microlocal hypoellipticity of pseudodifferential operators with \(C^ L\) coefficients. The notion of the \(C^ L\) functional class and the corresponding wave-front set \(WF_ L(u)\) has been introduced by \textit{L. Hörmander} in Commun. Pure Appl. Math. 24, 671-704 (1971; Zbl 0226.35019). When proving his main result the author constructs a parametrix and uses techniques influenced by Hörmander and Trèves. It concerns the microlocal parametrices for elliptic operators in \(L^ m_{\rho,\delta}\) and appropriate integrations by parts. - The statement of this paper generalizes a previous result of P. Bolley and J. Camus on microlocal hypoellipticity of differential operators with real analytic coefficients.