Garrigós: Poisson-like kernels in tube domains over light-cones

Garrigós, Gustavo:
Poisson-like kernels in tube domains over light-cones
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 13 (2002), fasc. n.3-4, p. 271-283, (English)
pdf (429 Kb), djvu (186 Kb). | MR1984106 | Zbl 1225.32005

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A family of holomorphic function spaces can be defined with reproducing kernels $B_{\alpha}(z,w)$, obtained as real powers of the Cauchy-Szegö kernel. In this paper we study properties of the associated Poisson-like kernels: $P_{\alpha}(z,w) = |B_{\alpha}(z,w)|^{2} / B_{\alpha}(z,z)$. 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.

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Referenze Bibliografiche