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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Limit properties of Poisson kernels of Siegel domains of type II


Author: Lawrence J. Dickson
Journal: Trans. Amer. Math. Soc. 219 (1976), 113-131
MSC: Primary 32M15; Secondary 31B25, 43A85
MathSciNet review: 0402134
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Abstract: The results of [1] concerning tight $ C_0^\ast$ limit of the Poisson kernel of a tube domain, as its parameter converges to a point on the cone boundary, are extended under certain hypotheses to Siegel domains of type II. In the case where the domain is polytopic, almost everywhere convergence of the $ {L^p}$ Poisson integral to its boundary values is obtained. Examples and further conjectures conclude the paper.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0402134-5
PII: S 0002-9947(1976)0402134-5
Keywords: Szego and Poisson kernels, cones, Hermitian forms, nilpotent groups, limit cones, tight $ C_0^\ast$ limit, weak-type operator
Article copyright: © Copyright 1976 American Mathematical Society