Convolution Properties of Orlicz Spaces on hypergroups

2021/01/18 by Ali Reza Bagheri Salec, Vishvesh Kumar, Salec, A. R. Bagheri +3
Mathematics · #43A15 #43A62 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2101.07366

openalex publication_date 2021/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, for a locally compact commutative hypergroup K and for a pair (Φ₁, Φ₂) 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∗ g to exist a.e., where f and g are arbitrary elements of Orlicz spaces L^Φ₁(K) and L^Φ₂(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 L¹_w(K) into L^Φ_w(K) for a weight w on a locally compact hypergroup K.

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