The Space of Pseudofunctions with Application to Disjointness Preserving Mappings

Let G be a locally compact group. In this short note, we study the space of pseudofunctions, denoted P F Φ ( G ) , associated with the Orlicz space L Φ ( G ) , where Φ is a Young function satisfying the Δ 2 -condition. We show that the dual of P F Φ ( G ) is a commutative Banach algebra. We also study the space of multipliers from the Orlicz Figà–Talamanca Herz algebra A Φ ( G ) (introduced by the authors in Indag Math 30:340–354, 2019) to the dual of P M Ψ ( G ) and use it to show that the space of bounded multipliers of A Φ ( G ) is a dual space. Finally, we characterize the disjointness preserving mappings between two Orlicz Figà–Talamanca Herz algebras.