Abstract
We prove almost everywhere semirestricted admissible convergence of the Poisson-Szegö integrals ofL p functions (1 <p ≤ ∞) on the Bergman-Shilov boundary of a Siegel domain. In the case of symmetric domains our theorem can be deduced from the results by Peter Sjögren on admissible convergence to the boundary of Poisson integrals on symmetric spaces, although semirestricted admissible convergence means here a more general approach to the boundary then originally defined for symmetric spaces.
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Communicated by Fulvio Ricci
R.C.P. was partially supported by NSF Grant 850577.
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Damek, E., Hulanicki, A. & Penney, R.C. Admissible convergence for the Poisson-Szegö integrals. J Geom Anal 5, 49–76 (1995). https://doi.org/10.1007/BF02926442
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DOI: https://doi.org/10.1007/BF02926442