Multiplication and composition operators between two Orlicz spaces

In this paper we consider composition operator $C_{\varphi} generated by nonsingular measurable transformation $T$ and multiplication operator $M_u$ generated by measurable function $u$ between two different Orlicz spaces, then we investigate boundedness, compactness and essential norm of multiplication and composition operators in term of properties of the mapping $\varphi$, the function $u$ and the measure space $(X, \Sigma, \mu)$.