Boundary behavior of harmonic forms on a rank one symmetric space

Abstract:

We study the boundary behavior of 1-forms on a rank-one symmetric space M satisfying the equations $d\omega = 0 = \delta \omega$; the role of boundary is played by a nilpotent (Iwasawa) group $\bar N$ of isometries of M. For forms satisfying certain ${H^p}$ integrability conditions, we obtain the existence of boundary values in an appropriate sense, characterize these boundary values by means of fractional and singular integral operators on the group $\bar N$, and exhibit explicit isomorphisms between ${H^p}$ spaces of forms on M and the ordinary ${L^p}$ spaces of functions on the group $\bar N$.