Convolution structures for an Orlicz space with respect to vector measures on a compact group

Abstract

The aim of this paper is to present some results about the space L^\Phi(\nu), where \nu is a vector measure on a compact (not necessarily abelian) group and \Phi is a Young function. We show that under certain conditions, the space L^\Phi(\nu) becomes an L^1(G)-module with respect to the usual convolution of functions. We also define one more convolution structure on L^\Phi(\nu).