Fine convergence and admissible convergence for symmetric spaces of rank one
Adam Korányi, John C. Taylor · Transactions of the American Mathematical Society · 1981
The connections between fine convergence in the sense of potential theory and admissible convergence to the boundary for quotients of eigenfunctions of the Laplace-Beltrami operator are investigated. This leads to a version of the local Fatou theorem on symmetric spaces of rank one which is considerably stronger than previously known results. The appendix establishes the relationship between harmonic measures on the intersection of the Martin boundaries of a domain and a subdomain.