Real analytic regularity of the Szegő projection on circular domains

So-Chin Chen

Vol. 148 (1991), No. 2, 225–235

DOI: 10.2140/pjm.1991.148.225

Abstract

In this note we show that D ⊆ ℂⁿ, n ≥ 2, is a smooth bounded pseudoconvex domain with real analytic defining function r(z) such that ∑ _k=1ⁿz_k(∂r∕∂z_k)≠0 holds near some x₀ ∈ bD, then if g ∈ C^ω(bD), we have that the Szegö projection of g, Sg, is real analytic near x₀. 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.

Mathematical Subject Classification 2000

Primary: 32H10

Secondary: 32A07

Milestones

Received: 10 April 1989

Published: 1 April 1991