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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 classicaldoi:10.1090/s0002-9939-2014-12393-8 fatcat:3ag3q6ha3nen7oxfzqx5trpmy4