Weak type estimates for spherical multipliers on noncompact symmetric spaces

TL;DR

This paper establishes precise weak type 1 bounds for spherical Fourier multipliers on noncompact symmetric spaces, advancing the understanding of harmonic analysis in these geometric settings.

Contribution

It provides sharp weak type 1 estimates for spherical multipliers, extending previous results by Anker and Ionescu.

Findings

Proved sharp weak type 1 bounds for spherical Fourier multipliers.

Extended harmonic analysis results on noncompact symmetric spaces.

Complemented earlier foundational work in the field.

Abstract

In this paper we prove sharp weak type 1 estimates for spherical Fourier multipliers on symmetric spaces of the noncompact type. This complements earlier results of J.-Ph. Anker and A.D. Ionescu.