Orlicz Modules over Coset Spaces of Compact Subgroups in Locally compact Groups

Abstract

Let $H$ be a compact subgroup of a locally compact group $G$ and let $m$ be the normalized $G$-invariant measure on homogeneous space $G/H$ associated with Weil's formula. Let $\phi$ be a Young function satisfying ${\Delta }_2$-condition. We introduce the notion of left module action of $L^1(G/H,m)$ on the Orlicz spaces $L^{\phi }(G/H,m).$ We also introduce a Banach left $L^1(G/H,m)$-submodule of $L^{\phi }(G/H,m).$

10 pages, Comments are welcome