Local Fatou theorem and area theorem for symmetric spaces of rank one

Local Fatou theorem and area theorem for symmetric spaces of rank one
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by A. Korányi and R. B. Putz PDF

Trans. Amer. Math. Soc. 224 (1976), 157-168 Request permission

The classical results for the unit disc mentioned in the title are extended to harmonic functions on symmetric spaces of rank one.

References

On the behavior of harmonic functions at the boundary

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Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
S. Helgason, Duality and Radon transform for symmetric spaces, Amer. J. Math. 85 (1963), 667–692. MR 158409, DOI 10.2307/2373114
Adam Korányi, Harmonic functions on Hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507–516. MR 277747, DOI 10.1090/S0002-9947-1969-0277747-0
Adam Korányi, Boundary behavior of Poisson integrals on symmetric spaces, Trans. Amer. Math. Soc. 140 (1969), 393–409. MR 245826, DOI 10.1090/S0002-9947-1969-0245826-X
Robert Byrne Putz, A generalized area theorem for harmonic functions on hermitian hyperbolic space, Trans. Amer. Math. Soc. 168 (1972), 243–258. MR 298049, DOI 10.1090/S0002-9947-1972-0298049-2
Elias M. Stein, On the theory of harmonic functions of several variables. II. Behavior near the boundary, Acta Math. 106 (1961), 137–174. MR 173019, DOI 10.1007/BF02545785
E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Mathematical Notes, No. 11, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0473215
A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587