On the Hausdorff-Young theorem for commutative hypergroups

• Autorzy: Sina Degenfeld-Schonburg
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 43A62: Hypergroups
• 43A32: Other transforms and operators of Fourier type

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 2
• Strony: 219-231

Daty

wydano

2013

Twórcy

autor

Sina Degenfeld-Schonburg

• Department of Mathematics, Munich University of Technology, 85748 Garching, Germany

Identyfikatory

DOI

10.4064/cm131-2-5