Cauchy-Szegö integrals for systems of harmonic functions

Adam Korányi; Stephen Vági

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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

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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.