Local Fatou theorem and area theorem for symmetric spaces of rank one
HTML articles powered by AMS MathViewer
- by A. Korányi and R. B. Putz
- Trans. Amer. Math. Soc. 224 (1976), 157-168
- DOI: https://doi.org/10.1090/S0002-9947-1976-0492068-2
- PDF | Request permission
Abstract:
The classical results for the unit disc mentioned in the title are extended to harmonic functions on symmetric spaces of rank one.References
- A. P. Calderón, On the behavior of harmonic functions at the boundary, Trans. Amer. Math. Soc. 68 (1950), 47-54. MR 11, 357.
- 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
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 224 (1976), 157-168
- MSC: Primary 22E30; Secondary 32M15, 43A85
- DOI: https://doi.org/10.1090/S0002-9947-1976-0492068-2
- MathSciNet review: 0492068