We study the Hausdorff-Young transform for a commutative hypergroup K and its dual space K̂ by extending the domain of the Fourier transform so as to encompass all functions in and respectively, where 1 ≤ p ≤ 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 K̂ is in general not a hypergroup itself.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-2-5,
author = {Sina Degenfeld-Schonburg},
title = {On the Hausdorff-Young theorem for commutative hypergroups},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {219-231},
zbl = {1281.43001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-2-5}
}
Sina Degenfeld-Schonburg. On the Hausdorff-Young theorem for commutative hypergroups. Colloquium Mathematicae, Tome 131 (2013) pp. 219-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-2-5/