  This article explores weighted $(L^p, L^q)$ inequalities for the Fourier
transform in rank one Riemannian symmetric spaces of noncompact type. We
establish both necessary and sufficient conditions for these inequalities to
hold. To prove the weighted Fourier inequalities, we apply restriction theorems
on symmetric spaces and utilize Calder{\'o}n's estimate for sublinear
operators. While establishing the necessary conditions, we demonstrate that
Harish-Chandra's elementary spherical functions play a crucial role in this
setting. Furthermore, we apply our findings to derive Fourier inequalities with
polynomial and exponential weights.
