Lp-boundedness of pseudo-differential operators on rank one Riemannian symmetric spaces of noncompact type

We study the boundedness properties of pseudo-differential operators associated with a sym-bol on rank one Riemannian symmetric spaces of noncompact type, where the symbol satisfies Hormander-type conditions near infinity. We use a generalized transference principle by Coifmann-Weiss to establish a connection between the L-p operator norm of the local part of the pseudo-differential operators on symmetric space with the Euclidean pseudo-differential operators. We also define a class of pseudo-differential operators with symbols having no regularity conditions in the space variable and explore their L-p-boundedness properties.