PROPER INCLUSION PROPERTIES OF MORREY SPACES

• Main Author: Imanuel Runtunuwu, Yohanes
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/83359
• Institution: Institut Teknologi Bandung

In this thesis, we study Morrey spaces along with their examples, discrete Morrey spaces, and the inclusion properties as well as proper inclusion properties of these spaces. The proper inclusion properties of Morrey spaces can be established by constructing a function that satisfies these properties. In 2019, E. Kikianty and C. Schwanke established an embedding from discrete Morrey spaces to continuous Morrey spaces. With similar idea, R. Yudatama (2024) achieved an embedding as well, but with a different definition. Based on this result, we can construct a function that satisfies the proper inclusion property of Morrey spaces via a sequence that satisfies the proper inclusion property of discrete Morrey spaces. In this thesis, we costructed a simpler function than Gunawan et al. obtained in 2018 and 2022. The sequence constructed may also be used in one part of the proof of the discrete Morrey space inclusion theorem by Haroske and Skrzypczak (2020). Additionally, in this thesis, we refine the embedding of discrete Morrey spaces into continuous Morrey spaces using a different norm definition than first form that introduced by Gunawan et al. (2018). Our results tells us that the constant Cp,q that we obtained are better than the constant Cp,q in previous results by Yudatama (2024).