Causal compactification and Hardy spaces

Let M = G/H be a irreducible symmetric space of Cayley type. Then M is diff eomorphic to an open and dense G-orbit in the Shilov boundary of G/K x G/K. This compactification of M is causal and can be used to give answers to qu estions in harmonic analysis on M. In particular we relate the Hardy space of M to the classical Hardy space on the bounded symmetric domain G/K x G/K . This gives a new formula for the Cauchy-Szego kernel for M.