$L^p$-boundedness of Pseudo differential operators on rank one Riemannian symmetric spaces of noncompact type

TL;DR

This paper investigates the boundedness of pseudo differential operators on rank one noncompact symmetric spaces, establishing conditions under which these operators are bounded on L^p spaces.

Contribution

It provides new L^p-boundedness results for pseudo differential operators on rank one symmetric spaces under Hörmander-type conditions.

Findings

Established L^p-boundedness for a class of pseudo differential operators.

Extended classical results to non-Euclidean symmetric spaces.

Identified symbol conditions ensuring boundedness.

Abstract

The aim of this paper is to study $L^p$-boundedness property of the pseudo differential operator associated with a symbol, on rank one Riemannian symmetric spaces of noncompact type, where the symbol satisfies H\"ormander-type conditions near infinity.