Abstract
Let K be a hypergroup. We characterize translation invariant operators from a vector-valued L1-space to a vector-valued Lp-space defined on K. Furthermore, for a commutative compact hypergroup K, we introduce and study the notion of character convolution transform of a Banach L1(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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