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Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces $L^{\phi }\left(G\right)$ and $L^{\psi }\left(G\right)$ on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set $(f,g)\in L^{\phi }\left(G\right)\times L^{\psi }\left(G\right):f*g$ is well defined on G is σ-c-lower porous in $L^{\phi }\left(G\right)\times L^{\psi }\left(G\right)$. This answers a question raised by Głąb and Strobin in 2010 in a more general setting of Orlicz spaces. We also prove a similar result for non-compact locally compact groups.

Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let $L^{\phi }\left(G\right)$ and $L^{\psi }\left(G\right)$ be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach $L^{\phi }\left(G\right)$-submodule X of $L^{\psi }\left(G\right)$, the multiplier space $Ho{m}_{L^{\phi }\left(G\right)}(L^{\phi }\left(G\right),X*)$ is a dual Banach space with predual $L^{\phi }\left(G\right)\bullet X:=\overline{span}ux:u\in L^{\phi }\left(G\right),x\in X$, where the closure is taken in the dual space of $Ho{m}_{L^{\phi }\left(G\right)}(L^{\phi }\left(G\right),X*)$. We also prove that if $\phi$ is a Δ₂-regular N-function, then $C{v}_{\phi }\left(G\right)$, the space of convolutors of $M^{\phi }\left(G\right)$, is identified with the dual of a Banach algebra of functions on G under pointwise...