On the Hausdorff-Young theorem for commutative hypergroups

Sina Degenfeld-Schonburg. "On the Hausdorff-Young theorem for commutative hypergroups." Colloquium Mathematicae 131.2 (2013): 219-231. <http://eudml.org/doc/284027>.

@article{SinaDegenfeld2013,
abstract = {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 $L^\{p\}(K,m)$ and $L^\{p\}(K̂,π)$ 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.},
author = {Sina Degenfeld-Schonburg},
journal = {Colloquium Mathematicae},
keywords = {hypergroups; Hausdorff-Young; inverse Hausdorff-Young; Fourier transform; inverse Fourier transform},
language = {eng},
number = {2},
pages = {219-231},
title = {On the Hausdorff-Young theorem for commutative hypergroups},
url = {http://eudml.org/doc/284027},
volume = {131},
year = {2013},
}

TY - JOUR
AU - Sina Degenfeld-Schonburg
TI - On the Hausdorff-Young theorem for commutative hypergroups
JO - Colloquium Mathematicae
PY - 2013
VL - 131
IS - 2
SP - 219
EP - 231
AB - 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 $L^{p}(K,m)$ and $L^{p}(K̂,π)$ 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.
LA - eng
KW - hypergroups; Hausdorff-Young; inverse Hausdorff-Young; Fourier transform; inverse Fourier transform
UR - http://eudml.org/doc/284027
ER -