The Inclusion Properties of Orlicz Sequence Spaces with Rao and Ren Norm
Lianna Rizky Gunawan, Al Azhary Masta, Siti Fatimah, Encum Sumiaty, Endang Cahya Mulyaning Asih, Sofihara Al Hazmy

Mathematics Study Program, Faculty of Mathematics and Natural Sciences Education, Indonesia University of Education
Jl. Dr. Setiabudi, Bandung, 40154, Indonesia

Abstract

The Orlicz space L_\Phi was first introduced in 1931 by Z. W. Birnbaum and W. Orlicz, which is an extention of Lebesgue space L_p with 1\leq p<\infty. Orlicz spaces has two different versions namely countinuous Orlicz space and Orlicz sequence space. The main objective of this study is to obtain the inclusion properties of Orlicz sequence spaces by using Rao and Ren norm defined on their generalized Orlicz spaces. The method used in this research is the properties of Young function and characteristic sequence norm. The result of this research is the inclusion properties of Orlicz sequence spaces with Rao and Ren norm.

Keywords: Orlicz space, invers of Young function, Orlicz sequence space, Young function, Inclusion property

Topic: Minisymposia Fourier Analysis and Integral Operators