Cauchy-Riemann equation in real ellipsoids of \(\mathbb{C}^n\)
The author solves the \(\overline\partial\)-equation with optimal \(L^p\) estimates in real ellipsoids of \(\mathbb{C}^n\). The main tools are the weighted integral formulas of \textit{B. Berndtsson} and \textit{M. Andersson} [Ann. Inst. Fourier 32, No. 3, 91-110 (1982; Zbl 0498.32001)] as well as the special support function constructed by \textit{K. Diederich}, \textit{J. E. Fornaess} and \textit{J. Wiegerinck} [Manuscr. Math. 56, 399-417 (1986; Zbl 0602.32006)]. The proof is based on elementary, but subtle, estimates of the corresponding integral kernels.
scientific article; zbMATH DE number 1279202