Bergman and Hardy spaces on model domains
In the first part of this paper we show that each function which belongs to the \(L^2\)-space of the boundary of a model domain and which is also a CR-distribution can be extended to a function holomorphic on the whole domain which belongs to the corresponding Hardy space \(H^2\). The extension is expressed in terms of a corresponding entire function with a growth condition depending on the shape of the model domain. In the following parts we consider Bergman and Szegő kernels on model domains and apply these results to determine the boundary limits of the Bergman kernel on the diagonal of a bounded pseudoconvex domain in \(\mathbb{C}^{n+1}\), that is \(h\)-extendible at a boundary point \(P\), using a reduction to the model case due to Boas, Straube and Yu.
scientific article; zbMATH DE number 1193074