Abstract
We prove that the difference between the Bergman and Szego projections on a bounded, pseudoconvex domain (with C ∞ boundary) is smoothing whenever the boundary Laplacian is subelliptic. An equivalent statement is that the Bergman projection can be represented as a composition of the Szego and harmonic Bergman projections (along with the restriction and Poisson extension operators) modulo an error that is smoothing. We give several applications to the study of optimal mapping properties for these projections and their difference.
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