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

中文翻译：

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Orlicz 空间关于紧群上向量测度的卷积结构

本文的目的是展示一些关于空间的结果$L^{\varPhi}(\nu),$在哪里$\nu$是紧致（不一定是阿贝尔）群的向量测度，并且$\varPhi$是一个 Young 函数。我们表明，在自然条件下，空间$L^{\varPhi }(\nu )$变成一个$L^{1}(G)$-模块关于通常的函数卷积。我们还定义了另一种卷积结构$L^{\varPhi }(\nu ).$