Multiplication operators on Orlicz and weighted Orlicz spaces
Let $(Ω,Σ,μ)$ be a $σ$-finite complete measure space, $τ:Ω\rightarrowΩ$ be a measurable transformation and $ϕ$ be an Orlicz function. In this article, first a necessary and sufficient condition for the bounded multiplication operator $M_u$ on Orlicz space $L^ϕ(Ω)$ induced by measurable function $u$ to be completely continuous has been established. Next by using Radon-Nikodym derivative $ω= \frac{d μ\circ τ^{-1}}{d μ}$, the multiplication operator $M_u$ on weighted Orlicz space $L^ϕ_ω(Ω)$ have been characterized.
math.FA↗