Norm preserving extensions of holomorphic functions defined on varieties in Cn

If V is an analytic set in a pseudoconvex domain Omega, we show there is always a pseudoconvex domain G subset of Omega that contains V and has the property that every bounded holomorphic function on Vextends to a bounded holomorphic function on G with the same norm. We find such a G for some particular analytic sets. When Omega is an operhedron we show there is a norm on holomorphic functions on V that can always be preserved by extensions to Omega. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This study demonstrates the existence of a pseudoconvex domain G in a pseudoconvex domain Omega, containing an analytic set V, where every bounded holomorphic function on V can be extended to G as a bounded holomorphic function with the same norm. Some specific cases are identified where such a G can be found. Furthermore, when Omega is an operhedron, a norm on holomorphic functions on V can always be preserved by extensions to Omega.