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

## TL;DR

This paper investigates the structure of Orlicz spaces associated with vector measures on compact groups, establishing conditions under which these spaces form modules with respect to convolution operations.

## Contribution

It introduces new convolution structures on Orlicz spaces with vector measures, expanding the understanding of their algebraic properties on compact groups.

## Key findings

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## 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).