Convolution properties of Orlicz spaces on hypergroups

Bagheri Salec, Ali Reza; Kumar, Vishvesh; Tabatabaie, Seyyed Mohammad

doi:10.1090/proc/15799

Convolution properties of Orlicz spaces on hypergroups
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by Ali Reza Bagheri Salec, Vishvesh Kumar and Seyyed Mohammad Tabatabaie

Proc. Amer. Math. Soc. 150 (2022), 1685-1696

DOI: https://doi.org/10.1090/proc/15799

Published electronically: January 20, 2022

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Abstract:

In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(\Phi _1, \Phi _2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the convolution $f\ast g$ to exist a.e., where $f$ and $g$ are arbitrary elements of Orlicz spaces $L^{\Phi _1}(K)$ and $L^{\Phi _2}(K)$, respectively. As an application, we present some equivalent conditions for compactness of a compactly generated locally compact abelian group. Moreover, we also characterize compact convolution operators from $L^1_w(K)$ into $L^\Phi _w(K)$ for a weight $w$ on a locally compact hypergroup $K$.

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