Regularity equivalence of the Szegö projection and the complex Green operator

Phillip S. Harrington, Marco M. Peloso, Andrew S. Raich
2014 Proceedings of the American Mathematical Society  
In this paper we prove that on a CR manifold of hypersurface type that satisfies the weak Y (q) condition, the complex Green operator G q is exactly (globally) regular if and only if the Szegö projections S q−1 , S q and a third orthogonal projection S q+1 are exactly (globally) regular. The projection S q+1 is closely related to the Szegö projection S q+1 and actually coincides with it if the space of harmonic (0, q + 1)-forms is trivial. This result extends the important and by now classical
more » ... d by now classical result by H. Boas and E. Straube on the equivalence of the regularity of the∂-Neumann operator and the Bergman projections on a smoothly bounded pseudoconvex domain. We also prove an extension of this result to the case of bounded smooth domains satisfying the weak Z(q) condition on a Stein manifold.
doi:10.1090/s0002-9939-2014-12393-8 fatcat:3ag3q6ha3nen7oxfzqx5trpmy4