Friedrich Haslinger
Bergman and Hardy spaces on model domains
(11 pages)
Abstract.
In the first part of this paper we show that each function
which belongs to the L2 - space of the boundary of a mo
del domain and which is also a CR-distribution can be
extended to a function holomorphic on whole domain
which belongs to
the corresponding Hardy space H2. 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 Szegö 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 Cn+1, that is
h-extendible at a boundary point P, using a reduction to the
model case due to Boas, Straube and Yu.
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