A Note on Boundedness Properties of Pseudo-Differential Operators on Rank One Symmetric Spaces of Noncompact Type

In this short note, we discuss the boundedness properties of the multiplier and pseudo-differential operators. More specifically, we first discuss multiplier and pseudo-differential operators theories in the classical setting. Then, we discuss multiplier results in symmetric space and their similarity and distinction with the corresponding results in Euclidean spaces. Finally, using the Helgason inversion formula, we define the pseudo-differential operators in noncompact type symmetric spaces and discuss its boundedness results.