Weighted composition operators on Orlicz-Sobolev spaces

For an open subset P of the Euclidean space R", a measurable non-singular transformation T : Omega -> Omega and a real-valued measurable function u on R", we study the weighted composition operator uC(T) : f bar right arrow u . (f circle T) on the Orlicz-Sobolev space W-1,W-psi(Omega) consisting of those functions of the Orlicz space L-psi (Omega) whose distributional derivatives of the first order belong to L-psi (Omega). We also discuss a sufficient condition under which uC(T) is compact.