Improved multiplier theorems on rank one noncompact symmetric spaces

Abstract

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a Mikhlin-H\"ormander condition. These are replaced by a requirement that parts of the multiplier function on the critical $p$ strip give rise to bounded Fourier multipliers.