Abstract: By using the Hba's expression of the inverse Abel transform for the Riemannian symmetric space SU^*(6)/SP(3),we obtain the analytic expression of the heat hernal e^1△ for this space, and then deduce the weak (1-1) boundedness of the maxiamal operator associated to the heat kernel,we obtain also the asymptotic behavious of the Riesz potential (△)^-1/2 near infinite and near the origin. Finally we study the integrability of the Riesz transform grad(△)^-1/2.

Key words: heat kernel, Riesz potential, Riesz transform, resolvant