CR extension for \(L^ p\) CR functions on a quadric submanifold of \(\mathbb C^ n\).
Let \(M\) be the CR submanifold of \(C^m_w\times C^d_z\) defined by equations \(\Re z_i=q_i(w,\bar w),\; i=1,...,d\), with \(q_i\) a Hermitian symmetric form in \(C^m_w\). Denote by CR\(^p(M)\) the space of \(L^p\) CR functions on \(M\). The author shows that functions of CR\(^p(M)\) extend to \(H^p\) function on the interior of the convex hull of \(M\). This result is a global version of the one obtained with \textit{A. Nagel} [Pac. J. Math. 167, No. 1, 1--47 (1995; Zbl 0848.32015)]. As part of the proof, he establishes a semi-global version of the approximation theorem of \textit{M. S. Baouendi} and \textit{F. Treves} [Ann. Math. (2) 113, No. 2, 387--421; (1981; Zbl 0491.35036)] for submanifolds which are graphs of functions with polynomial growth.
scientific article; zbMATH DE number 1818912