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^Φ(ν), where νis a vector measure on a compact (not necessarily abelian) group and Φis a Young function. We show that under certain conditions, the space L^Φ(ν) becomes an L^1(G)-module with respect to the usual convolution of functions. We also define one more convolution structure on L^Φ(ν).

11 pages