Extension of bounded holomorphic functions in convex domains (Q5947076)

The authors prove that if \(D\) is a smooth convex domain of finite type \(m\) and \(A\) a complex affine linear hypersurface such that \(D':=D \cap A\) then there is a bounded linear extension operator \(E : H^\infty (D') \rightarrow H^\infty(D)\). The authors construct the extension operator in terms of an integral operator of Andersson-Berndtsson type using the support functions for convex domains of finite type.