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 ϕ be a Young function satisfying ∆2-condition. We introduce the notion of left module action of L 1 (G/H, m) on the Orlicz spaces L ϕ (G/H, m). We also introduce a Banach left L 1 (G/H, m)submodule of L ϕ (G/H, m).