Geodesic
On the Hausdorff–Young theorem for commutative hypergroups
Sina Degenfeld-Schonburg1
1 Department of Mathematics Munich University of Technology 85748 Garching, Germany
Colloquium Mathematicum, Tome 131 (2013) no. 2, pp. 219-231.

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We study the Hausdorff–Young transform for a commutative hypergroup $K$ and its dual space $\hat{K}$ by extending the domain of the Fourier transform so as to encompass all functions in $L^p(K,m)$ and $L^p(\hat{K},\pi)$ respectively, where $1\leq p \leq 2$. Our main theorem is that those extended transforms are inverse to each other. In contrast to the group case, this is not obvious, since the dual space $\hat{K}$ is in general not a hypergroup itself.
DOI : 10.4064/cm131-2-5
Keywords: study hausdorff young transform commutative hypergroup its dual space hat extending domain fourier transform encompass functions m hat respectively where leq leq main theorem those extended transforms inverse each other contrast group obvious since dual space hat general hypergroup itself

Sina Degenfeld-Schonburg 1

1 Department of Mathematics Munich University of Technology 85748 Garching, Germany 
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Sina Degenfeld-Schonburg. On the Hausdorff–Young theorem
 for commutative hypergroups. Colloquium Mathematicum, Tome 131 (2013) no. 2, pp. 219-231. doi : 10.4064/cm131-2-5. http://geodesic.mathdoc.fr/articles/10.4064/cm131-2-5/

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