Acta Mathematica Vietnamica

Let K be a hypergroup. We characterize translation invariant operators from a vector-valued $L^1$-space to a vector-valued $L^p$-space defined on $K$. Furthermore, for a commutative compact hypergroup $K$, we introduce and study the notion of character convolution transform of a Banach $L^1(K)$-module $M$. Several characterizations of multipliers on $M$ are given. We also prove an analogue of the Schoenberg-Eberlein theorem for the character convolution transform.

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