Parabolic exhaustions for strictly convex domains.
A family of holomorphic function spaces can be defined with reproducing kernels , obtained as real powers of the Cauchy-Szegö kernel. In this paper we study properties of the associated Poisson-like kernels: . In particular, we show boundedness of associated maximal operators, and obtain formulas for the limit of Poisson integrals in the topological boundary of the cone.
A complete characterization of proper holomorphic mappings between domains from the class of all pseudoconvex Reinhardt domains in ℂ² with the logarithmic image equal to a strip or a half-plane is given.
We present a result on the existence of some kind of peak functions for ℂ-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for A(D) under proper holomorphic mappings. Additionally, we present a description of the set of peak points in the class of bounded pseudoconvex Reinhardt domains.