Convergence of Poisson integrals on generalized upper half-planes

Convergence of Poisson integrals on generalized upper half-planes
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Trans. Amer. Math. Soc. 136 (1969), 109-123

DOI: https://doi.org/10.1090/S0002-9947-1969-0234014-9

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References

Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
A. W. Knapp, Fatou’s theorem for symmetric spaces. I, Ann. of Math. (2) 88 (1968), 106–127. MR 225938, DOI 10.2307/1970557
Adam Korányi, The Poisson integral for generalized half-planes and bounded symmetric domains, Ann. of Math. (2) 82 (1965), 332–350. MR 200478, DOI 10.2307/1970645
S. Helgason and A. Korányi, A Fatou-type theorem for harmonic functions on symmetric spaces, Bull. Amer. Math. Soc. 74 (1968), 258–263. MR 229179, DOI 10.1090/S0002-9904-1968-11912-3

Fatou’s theorem for generalized halfplanes

Adam Korányi and Joseph A. Wolf, Realization of hermitian symmetric spaces as generalized half-planes, Ann. of Math. (2) 81 (1965), 265–288. MR 174787, DOI 10.2307/1970616
E. M. Stein, Note on the boundary values of holomorphic functions, Ann. of Math. (2) 82 (1965), 351–353. MR 188485, DOI 10.2307/1970646
Norman J. Weiss, Almost everywhere convergence of Poisson integrals on tube domains over cones, Trans. Amer. Math. Soc. 129 (1967), 283–307. MR 222330, DOI 10.1090/S0002-9947-1967-0222330-4

Almost everywhere convergence of Poisson integrals on tube domains over cones

A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

Maximal functions and Fatou’s theorem

E. M. Stein and N. J. Weiss, Convergence of Poisson integrals for bounded symmetric domains, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1160–1162. MR 229856, DOI 10.1073/pnas.60.4.1160