Parasar Mohanty

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.

The purpose of this note is to construct an example of a discrete non-abelian group $G$ and a subset $E$ of $G$, not contained in any abelian subgroup, that is a completely bounded $\Lambda (p)$ set for all $p<\infty ,$ but is neither a Leinert set nor a weak Sidon set.