Holomorphic reproducing kernels in Reinhardt domains

Harold Philip Boas

Vol. 112 (1984), No. 2, 273–292

DOI: 10.2140/pjm.1984.112.273

Abstract

The orthogonal projection P₀ : L²(Ω) → L²(Ω) ∩ {holomorphic functions} (the Bergman projection) is studied, together with its analogue P_s : W^s(Ω) → W^s(Ω)  ∩  {holomorphic functions}, for smooth bounded pseudoconvex complete Reinhardt domains Ω ⊂ Cⁿ. It is shown that P_s maps the Sobolev space W^r(Ω) boundedly into itself for each r ≥ s. Explicit formulas are computed for the representing kernel functions for the case of the ball.

Mathematical Subject Classification 2000

Primary: 32H10

Secondary: 46E20

Milestones

Received: 9 March 1982

Revised: 20 December 1982

Published: 1 June 1984