Real analytic regularity of the Bergman and Szegö projections on decoupled domains (Q1321002)

We combine the local analytic regularity results of the \(\overline\partial\)-Neumann problem at strictly pseudoconvex points with rotational symmetries to obtain global analytic regularity of the \(\overline\partial\)-Neumann problem and the Bergman projection on some classes of bounded weakly pseudoconvex domains with real analytic boundaries. Examples include the holomorphically decoupled, or the decoupled Hartogs domains in \(\mathbb{C}^ 2\). Similar situation for the Szegö projection is also discussed here.