L2 Oka–Cartan theory

Abstract

Oka–Cartan theory is mainly concerned with the ideals of holomorphic functions on pseudoconvex domains over ℂn. To describe how one can find global generators of the ideals, the application of extension theorems and division theorems is indispensable. From the viewpoint of the ∂̄ -equations, these questions amount to solving those of very special type. Making use of the specific forms of these ∂̄ -equations, they are solved with precise L2 norm estimates, yielding optimal quantitative variants of Oka–Cartan theorems.