We consider several types of multipliers on the Banach algebras related to the homogeneous space G/H, where G is a locally compact group and H is a compact subgroup. Among other things, we show that an analogue of Wendel’s result holds for these types of Banach algebras only when H is normal. We then investigate the characterization of all multipliers from \(L^1(G/H)\) into \(L^p(G/H)\) when they considered as left \(L^1(G/H)\)-module. Finally, we give some result for the case when G is compact and H is closed.

中文翻译：

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$$\hbox {L}^p$$ L p -Spaces for Homogeneous Spaces 上的乘数

我们考虑与齐次空间G / H相关的 Banach 代数上的几种类型的乘子，其中G是局部紧群，H是紧子群。除其他外，我们表明，只有当H为正态时，Wendel 结果的类似物才适用于这些类型的 Banach 代数。然后我们研究了从\(L^1(G/H)\)到\(L^p(G/H)\)的所有乘数的表征，当它们被认为是左\(L^1(G/H)\) ) -模块。最后，我们给出了G紧致且H闭合的情况的一些结果。