Fornaess, John Erik; Wiegerinck, Jan A holomorphic reproducing kernel for Kohn-Nirenberg domains in \({\mathbb C}^ 2\). (English) Zbl 0639.32002 Math. Scand. 62, No. 1, 44-58 (1988). Let \(\Omega\) be a truncated Kohn-Nirenberg domain in \({\mathbb{C}}^ 2:\) \(\Omega =\{w\in {\mathbb{C}}^ 2:\) \(Re w_ 2+P(w_ 1)<0\}\cap \{| w| <R\},\) where P is a real valued homogeneous polynomial which is strictly subharmonic for \(w\neq 0\). A Cauchy-Fantappiè kernel for \(\Omega\) is constructed and its properties are investigated. The construction is based on a modification of the Leray map for \(\Omega\) as constructed by the first author in Ann. Math., II. Ser. 123, 335-345 (1986; Zbl 0589.32038). It is shown that this kernel reproduces \(H(\Omega)\cap C(\Omega ^ -)\) and maps C(b\(\Omega)\) into H(\(\Omega)\), H denoting holomorphic functions and C denoting continuous functions. Reviewer: J.E.Fornaess Cited in 1 Document MSC: 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) Keywords:Cauchy-Fantappiè kernel; Kohn-Nirenberg domains Citations:Zbl 0589.32038 PDFBibTeX XMLCite \textit{J. E. Fornaess} and \textit{J. Wiegerinck}, Math. Scand. 62, No. 1, 44--58 (1988; Zbl 0639.32002) Full Text: DOI EuDML