Optimal \(L^ p\) estimates for the \(\bar \partial\)-equation on complex ellipsoids in \(\mathbb{C}^ n\) (Q1313569)

\(L^ p\)-estimates for solutions of \(\overline \partial\) on ellipsoids of \(\mathbb{C}^ n\) are stated here. Estimations for strongly pseudoconvex domains as well as for weakly pseudoconvex of finite type in \(\mathbb{C}^ 2\) are classical. We also mention \textit{M. Derridj} and \textit{D. Tartekoff}, J. Geom. Anal. 3, 141- 151 (1993) for \(L^ 2\)-estimates on ``completely decoupled pseudoconvex'' domains. We finally remark that some counterexamples by Christ and Geller to analytic hypoellipticity (even in the finite type case) suggest that estimates for pseudoconvex domains should fail to held in general.