Abstract
Let D be a smoothly bounded pseudoconvex domain in C n , n ≥ 2, with real analytic boundary. In this paper we show that □ b is globally analytic hypoelliptic if D is either circular satisfying Σ n j=1 z j ∂r/∂z j (z) ≠ 0 near the boundary bD, where r(z) is a defining function for D, or Reinhardt.