Exact regularity of the Bergman and Szegö projections on domains with partially transverse symmetries Academic Article uri icon

abstract

  • If D is a smooth bounded pseudoconvex domain in Cn 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 Wr(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 C2, 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.

author list (cited authors)

  • Boas, H. P., Chen, S., & Straube, E. J.

citation count

  • 11

publication date

  • December 1988