The boundary regularity of the solution of the ∂-equation in the product of strictly pseudoconvex domains

Piotr Jakóbczak

Vol. 121 (1986), No. 2, 371–381

DOI: 10.2140/pjm.1986.121.371

Abstract

Let D be a strictly pseudoconvex domain in Cⁿ. We prove that for every ∂-closed differential (0,q)-form f, q ≥ 1, with coefficients of class 𝒞^∞(D × D), and continuous in the set D ×D ∖ Δ(D), the equation ∂u = f admits a solution u with the same boundary regularity properties. As an application, we prove that certain ideals of analytic functions in strictly pseudoconvex domains are finitely generated.

Mathematical Subject Classification 2000

Primary: 32F20

Secondary: 32E25, 35N15

Milestones

Received: 10 June 1984

Revised: 1 October 1984

Published: 1 February 1986