Orlicz Function Spaces and Composition Operator

Abstract

In our dissertation we present here the salient features from the theory of Orlicz function spaces, LÖ(Ù), generated by the Young’s function Ö on an arbitrary ó−finite measurable spaces Ù. We will discussed these are the Banach spaces equipped with the equivalent orlicz and gauge norms.Finally we study the Composition operators Cô between Orlicz spaces LÖ(Ù) generated by measurable and non-singular transformations ô from Ù into itself. We also investigate the Boundedness and compactness of the composition operators on the Orlicz spaces by using different types of Ä2 conditions of the orlicz function Ö.