  First, we correct the proof presented in [Abimbola Abolarinwa, Kamilu Rauf,
Songting Yin, Sharp $L^{p}$ Hardy type and uncertainty principle inequalities
on the sphere, Journal of Mathematical Inequalities, 13, 4 (2019), 1011 - 1022]
and obtain a correct sharp version of an $L^{p}$ Hardy inequality on the sphere
$\mathbb{S}^{n}$ for all $2\leq p<n$. Secondly, we prove sharp critical
exponent $L^{n}$ inequalities on the sphere $\mathbb{S}^{n}$ in
$\mathbb{R}^{n+1}$, $n\geq 2$. The singularity in this problem is the geodesic
distance from an arbitrary point on the sphere.
