  It has been shown in "On the Hausdorff-Young theorem for commutative
hypergroups" by Sina Degenfeld-Schonburg, that one can extend the domain of
Fourier transform of a commutative hypergroup $K$ to $L^p(K)$ for $1\leq p \leq
2$, and the Hausdorff-Young inequality holds true for these cases. In this
article, we examine the structure of non-zero functions in $L^p(K)$ for which
equality is attained in the Hausdorff-Young inequality, for $1<p<2$, and
further provide a characterization for the basic uncertainty principle for
commutative hypergroups with non-trivial centre.
