An Inclusion Property of Discrete Orlicz-Morrey Spaces of Sawano - Sugano - Tanaka^s version
Al Azhary Masta1, Endang Cahya Mulyaning2, Siti Fatimah3, Cece Kustiawan4

Mathematics Study Program, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi 229, Bandung 40154, Indonesia

Abstract

The Orlicz--Morrey spaces are generalizations of Orlicz spaces and Morrey spaces. There are two types of Orlicz-Morey spaces, namely continuous Orlicz-Orlicz spaces and sequence Orlicz-Orlicz spaces. Furtnermore, there are three versions of Orlicz -Morrey spaces, i.e:Nakai ^s, Sawano -Sugano -Tanaka ^s and Deringoz -Guliyev -Samko ^s versions. The inclusion properties of Orlicz spaces, weighted Orlicz spaces, Morrey spaces, and Orlicz--Morrey spaces, discrete Orlicz-Morrey of Nakai^s version are well known. In this research, we will investigate the inclusion properties of discrete Orlicz - Morrey spaces of Sawano - Sugano - Tanaka^s version. The novelty of this paper is to obtain some sufficient and necessary conditions for the inclusion properties of these spaces. The inclusion properties of these spaces is generalizes inclusion properties of discrete Morrey spaces. One of the key to proof of our results is to use the norm of the characteristic sequence in Z.

Keywords: Inclusion property, Orlicz - Morrey spaces, Discrete weak Orlicz - Morrey spaces.

Topic: Mathematic