Abstract
If D is a smooth bounded pseudoconvex domain in C n that has symmetries transverse on the complement of a compact subset of the boundary consisting of points of finite type, then the Bergman projection for D maps the Sobolev space W r (D) continuously into itself and the Szegö projection maps the Sobolev space Wsur(bD) continuously into itself. If D has symmetries, coming from a group of rotations, that are transverse on the complement of a B-regular subset of the boundary, then the Bergman projection, the Szegö projection, and the {Mathematical expression}-Neumann operator on (0, 1)-forms all exactly preserve differentiability measured in Sobolev norms. The results hold, in particular, for all smooth bounded strictly complete pseudoconvex Hartogs domains in C 2 , as well as for Sibony's counterexample domain that fails to have sup-norm estimates for solutions of the {Mathematical expression}-equation. © 1988 Springer-Verlag.