Fourier Integral Operators on Noncompact Symmetric Spaces of Real Rank One

Abstract

Let X=G/K be a noncompact symmetric space of real rank one. The purpose of this paper is to investigate Lp boundedness properties of a certain class of radial Fourier integral operators on the space X. We will prove that if uτ is the solution at some fixed time τ of the natural wave equation on X with initial data f and g and 1