Equality in Hausdorff–Young for hypergroups

Abstract

It was shown in [Colloq. Math. 131(2), 219--231 (2013)] that one can extend the domain of Fourier transform of a commutative hypergroup K to \(L^p(K)\) for \(1\le p \le 2\), 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 center.