A note on growth of Fourier transforms and Moduli of continuity on Damek Ricci spaces

TL;DR

This paper investigates the growth behavior of Fourier transforms in relation to the modulus of continuity on Damek-Ricci spaces, extending similar results to rank one symmetric spaces.

Contribution

It provides new bounds on Fourier transform growth linked to the modulus of continuity specifically on Damek-Ricci spaces, with extensions to symmetric spaces of rank one.

Findings

Bounded growth of Fourier transforms established

Results extended to rank one symmetric spaces

Analogues of classical results derived for Damek-Ricci spaces

Abstract

We obtain results related to boundedness of the growth of Fourier transform by the modulus of continuity on Damek-Ricci spaces. For noncompact riemannian symmetric spaces of rank one, analogues of all the results follow the same way.