Abstract
In this note we show that D ⊆ ℂ n , n ≥ 2, is a smooth bounded pseudoconvex domain with real analytic defining function r(z) such that Σ k=1 n Z k (∂r/∂ zk ) ≠ 0 holds near some x 0 ∈ bD, then if g ∈ C ω (bD), we have that the Szegö projection of g, Sg, is real analytic near x 0 . In particular if D is a smooth bounded complete Reinhardt (or Reinhardt) pseudoconvex domain with real analytic boundary, then the Szegö projection S preserves real analyticity globally. © 1991 by Pacific Journal of Mathematics.