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Poisson-like kernels in tube domains over light-cones

Gustavo Garrigós (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A family of holomorphic function spaces can be defined with reproducing kernels B α z , w , obtained as real powers of the Cauchy-Szegö kernel. In this paper we study properties of the associated Poisson-like kernels: P α z , w = B α z , w 2 / B α z , z . 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.

Proper holomorphic mappings vs. peak points and Shilov boundary

Łukasz Kosiński, Włodzimierz Zwonek (2013)

Annales Polonici Mathematici

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.

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