Convolution operators on Banach–Orlicz algebras

Abstract

For a locally compact group G, let $$\mathcal{L}^{\Phi}$$(G) and $$\mathcal{L}_\omega^{\Phi}$$(G) be Orlicz and weighted Orlicz spaces, respectively, where Φ is a Young function and ω is a weight on G. We study the harmonic and convolution operators on Orlicz and weighted Orlicz spaces. We prove that under some conditions the harmonic operators on $$\mathcal{L}^{\Phi}$$(G) and $$\mathcal{L}_\omega^{\Phi}$$(G) are compact. We characterize convolution operators on Orlicz and weighted Orlicz spaces $$\mathcal{L}^{\Phi}$$(G) and $$\mathcal{L}_\omega^{\Phi}$$(G).