Several Properties of Discrete Orlicz Spaces Pradipta Swiantana Prayoga, Siti Fatimah, and Al Azhary Masta
Universitas Pendidikan Indonesia
Abstract
Introduced by Z. W. Birnbaum and W. Orlicz in 1931, Orlicz spaces are generalization of the Lebesgue spaces. There are two kinds version of Orlicz spaces which are continuous Orlicz spaces denoted by \(L_Φ\) and discrete Orlicz spaces denoted by \(l_Φ\). The properties of \(L_Φ\) spaces are already known. The aim of this study is to discuss the properties of discrete Orlicz spaces. We will see that the properties of continuous Orlicz spaces are also valid on discrete Orlicz spaces. Methods in this research are by using the properties of Young function and Luxemburg Norm. The result of this research is to show that several properties of continuous Orlicz space are also valid on discrete Orlicz space.
