Equality in Hausdorff–Young for hypergroups
Tóm tắt
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
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