Holomorphic Approximation on Certain Weakly Pseudoconvex Domains in <i>C</i>ⁿ

Abstract

The purpose of this paper is to study the Mergelyan approximation property in L p and C k -scales on certain weakly pseudoconvex domains of finite/infinite type in C n . At the heart of our results lies the solvability of the additive Cousin problem with bounds as well as estimates of the ∂ ¯ -equation in the corresponding topologies.

Keywords

• mergelyan property
• weakly pseudoconvex domains
• additive cousin problem