Limit properties of Poisson kernels of Siegel domains of type II

Dickson, Lawrence J.

doi:10.1090/S0002-9947-1976-0402134-5

Limit properties of Poisson kernels of Siegel domains of type II
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by Lawrence J. Dickson PDF

Trans. Amer. Math. Soc. 219 (1976), 113-131 Request permission

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.

References

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