INCLUSION PROPERTIES OF ORLICZ–MORREY SPACES

• Main Author: AZHARY MASTA (NIM: 30113003), AL
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/25291
• Institution: Institut Teknologi Bandung

Orlicz-Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by E. Nakai in 2004. These spaces are one of important topics in mathematical analysis, particularly in harmonic analysis. There are three versions of Orlicz-Morrey spaces, i.e: Nakai's (2004), Sawano-Sugano-Tanaka's (2012), and Deringoz-Guliyev-Samko's (2014) versions. In this dissertation, we would like to obtain the inclusion properties of Orlicz-Morrey spaces of Nakai's and Sawano-Sugano-Tanaka's versions. We start by reproving the sufficient and necessary conditions for the inclusion properties of Orlicz spaces, Morrey spaces, generalized Morrey spaces, and their weak type. Next, similar results for Orlicz-Morrey spaces and weak Orlicz-Morrey spaces are also obtained. Our results complete those obtained by Nakai (2004) and also generalize the inclusion properties of Orlicz spaces and Morrey spaces. One of the keys to prove of our results is to estimate the norms of the characteristic functions of the balls in R^n. In addition, we prove the sufficient and necessary conditions for generalized Ho ̈lder 's inequality in Orlicz spaces, in Morrey spaces, in generalized Morrey spaces, in Orlicz-Morrey spaces, and in their weak type versions, which are obtained through norm estimates for the characteristic functions of balls in R^n.